Ambrosio, Luigi
Overview
Works:  60 works in 375 publications in 3 languages and 7,050 library holdings 

Genres:  Conference papers and proceedings Textbooks 
Roles:  Author, Editor, Creator, Commentator, Thesis advisor, Other, Opponent 
Classifications:  QA3, 515.64 
Publication Timeline
.
Most widely held works by
Luigi Ambrosio
Gradient flows : in metric spaces and in the space of probability measures by
Luigi Ambrosio(
Book
)
54 editions published between 2004 and 2008 in English and German and held by 394 WorldCat member libraries worldwide
"This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the space of probability measures on a separable Hilbert space, endowed with the KantorovichRubinsteinWasserstein distance."Jacket
54 editions published between 2004 and 2008 in English and German and held by 394 WorldCat member libraries worldwide
"This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the space of probability measures on a separable Hilbert space, endowed with the KantorovichRubinsteinWasserstein distance."Jacket
Mathematical aspects of evolving interfaces : lectures given at the C.I.M.C.I.M.E. joint Eurosummer school held in Madeira,
Funchal, Portugal, July 39, 2000 by
Luigi Ambrosio(
Book
)
23 editions published in 2003 in English and held by 305 WorldCat member libraries worldwide
Interfaces are geometrical objects modelling free or moving boundaries and arise in a wide range of phase change problems in physical and biological sciences, particularly in material technology and in dynamics of patterns. Especially in the end of last century, the study of evolving interfaces in a number of applied fields becomes increasingly important, so that the possibility of describing their dynamics through suitable mathematical models became one of the most challenging and interdisciplinary problems in applied mathematics. The 2000 Madeira school reported on mathematical advances in some theoretical, modelling and numerical issues concerned with dynamics of interfaces and free boundaries. Specifically, the five courses dealt with an assessment of recent results on the optimal transportation problem, the numerical approximation of moving fronts evolving by mean curvature, the dynamics of patterns and interfaces in some reactiondiffusion systems with chemicalbiological applications, evolutionary free boundary problems of parabolic type or for NavierStokes equations, and a variational approach to evolution problems for the GinzburgLandau functional
23 editions published in 2003 in English and held by 305 WorldCat member libraries worldwide
Interfaces are geometrical objects modelling free or moving boundaries and arise in a wide range of phase change problems in physical and biological sciences, particularly in material technology and in dynamics of patterns. Especially in the end of last century, the study of evolving interfaces in a number of applied fields becomes increasingly important, so that the possibility of describing their dynamics through suitable mathematical models became one of the most challenging and interdisciplinary problems in applied mathematics. The 2000 Madeira school reported on mathematical advances in some theoretical, modelling and numerical issues concerned with dynamics of interfaces and free boundaries. Specifically, the five courses dealt with an assessment of recent results on the optimal transportation problem, the numerical approximation of moving fronts evolving by mean curvature, the dynamics of patterns and interfaces in some reactiondiffusion systems with chemicalbiological applications, evolutionary free boundary problems of parabolic type or for NavierStokes equations, and a variational approach to evolution problems for the GinzburgLandau functional
Optimal transportation and applications : lectures given at the C.I.M.E. summer school held in Martina Franca, Italy, September
28, 2001 by C.I.M.E Course on Optimal Transportation and Applications(
Book
)
18 editions published in 2003 in English and held by 303 WorldCat member libraries worldwide
Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: MongeAmpre and MongeKantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory
18 editions published in 2003 in English and held by 303 WorldCat member libraries worldwide
Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: MongeAmpre and MongeKantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory
Functions of bounded variation and free discontinuity problems by
Luigi Ambrosio(
Book
)
18 editions published between 2000 and 2006 in English and held by 286 WorldCat member libraries worldwide
"This book deals with a class of mathematical problems which involve the minimization of the sum of a volume and a surface energy and have lately been referred to as 'free discontinuity problems'. The aim of this book is twofold: The first three chapters present all the basic prerequisites for the treatment of free discontinuity and other variational problems in a systematic, general, and selfcontained way. In the later chapters, the reader is introduced to the theory of free discontinuity problems, to the space of special functions of bounded variation, and is presented with a detailed analysis of the MumfordShah image segmentation problem. Existence, regularity and qualitative properties of solutions are explained and a survey is given on the current knowledge of this challenging mathematical problem. The theory embodies classical problems, e.g. related to phase transitions, or fracture and plasticity in continuum mechanics, as well as more recent ones like edge detection in image analysis. This book provides the reader with a solid introduction to the field, written by principle contributors to the theory."Publisher's description
18 editions published between 2000 and 2006 in English and held by 286 WorldCat member libraries worldwide
"This book deals with a class of mathematical problems which involve the minimization of the sum of a volume and a surface energy and have lately been referred to as 'free discontinuity problems'. The aim of this book is twofold: The first three chapters present all the basic prerequisites for the treatment of free discontinuity and other variational problems in a systematic, general, and selfcontained way. In the later chapters, the reader is introduced to the theory of free discontinuity problems, to the space of special functions of bounded variation, and is presented with a detailed analysis of the MumfordShah image segmentation problem. Existence, regularity and qualitative properties of solutions are explained and a survey is given on the current knowledge of this challenging mathematical problem. The theory embodies classical problems, e.g. related to phase transitions, or fracture and plasticity in continuum mechanics, as well as more recent ones like edge detection in image analysis. This book provides the reader with a solid introduction to the field, written by principle contributors to the theory."Publisher's description
Calculus of variations and partial differential equations : topics on geometrical evolution problems and degree theory by
Luigi Ambrosio(
Book
)
15 editions published between 1999 and 2000 in English and held by 255 WorldCat member libraries worldwide
"The link between Calculus of Variations and Partial Differential Equations has always been strong, because variational problems produce, via their EulerLagrange equation, a differential equation and, conversely, a differential equation can often be studied by variational methods. At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on a classical topic in a selfcontained presentation accessible to Ph. D. students, bridging the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and illustrates the 2way interaction of problems and methods."Jacket
15 editions published between 1999 and 2000 in English and held by 255 WorldCat member libraries worldwide
"The link between Calculus of Variations and Partial Differential Equations has always been strong, because variational problems produce, via their EulerLagrange equation, a differential equation and, conversely, a differential equation can often be studied by variational methods. At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on a classical topic in a selfcontained presentation accessible to Ph. D. students, bridging the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and illustrates the 2way interaction of problems and methods."Jacket
Topics on analysis in metric spaces by
Luigi Ambrosio(
Book
)
11 editions published between 2004 and 2009 in English and held by 245 WorldCat member libraries worldwide
Based on lecture notes from the Scuola Normale this book presents the main mathematical prerequisites for analysis in metric spaces. Supplemented with exercises of varying difficulty it is suitable for a graduatelevel short course for applied mathematicians and engineers
11 editions published between 2004 and 2009 in English and held by 245 WorldCat member libraries worldwide
Based on lecture notes from the Scuola Normale this book presents the main mathematical prerequisites for analysis in metric spaces. Supplemented with exercises of varying difficulty it is suitable for a graduatelevel short course for applied mathematicians and engineers
Calculus of variations and nonlinear partial differential equations : lectures given at the C.I.M.E. Summer School held in
Cetraro, Italy, June 27July 2, 2005 by CIME Session "Enumerative Invariants in Algebraic Geometry and String Theory"(
Book
)
15 editions published in 2008 in English and held by 233 WorldCat member libraries worldwide
This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo
15 editions published in 2008 in English and held by 233 WorldCat member libraries worldwide
This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo
Nonlinear PDE's and applications : C.I.M.E. Summer School, Cetraro, Italy, 2008 by
Stefano Bianchini(
Book
)
14 editions published in 2011 in English and held by 171 WorldCat member libraries worldwide
This volume collects the notes of the CIME course "Nonlinear PDE's and applications" held in Cetraro (Italy) on June 2328, 2008. It consists of four series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), and Cédric Villani (Ecole Normale Superieure de Lyon). They presented a broad overview of farreaching findings and exciting new developments concerning, in particular, optimal transport theory, nonlinear evolution equations, functional inequalities, and differential geometry. A sampling of the main topics considered here includes optimal transport, HamiltonJacobi equations, Riemannian geometry, and their links with sharp geometric/functional inequalities, variational methods for studying nonlinear evolution equations and their scaling properties, and the metric/energetic theory of gradient flows and of rateindependent evolution problems. The book explores the fundamental connections between all of these topics and points to new research directions in contributions by leading experts in these fields
14 editions published in 2011 in English and held by 171 WorldCat member libraries worldwide
This volume collects the notes of the CIME course "Nonlinear PDE's and applications" held in Cetraro (Italy) on June 2328, 2008. It consists of four series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), and Cédric Villani (Ecole Normale Superieure de Lyon). They presented a broad overview of farreaching findings and exciting new developments concerning, in particular, optimal transport theory, nonlinear evolution equations, functional inequalities, and differential geometry. A sampling of the main topics considered here includes optimal transport, HamiltonJacobi equations, Riemannian geometry, and their links with sharp geometric/functional inequalities, variational methods for studying nonlinear evolution equations and their scaling properties, and the metric/energetic theory of gradient flows and of rateindependent evolution problems. The book explores the fundamental connections between all of these topics and points to new research directions in contributions by leading experts in these fields
Modelling and optimisation of flows on networks : Cetraro, Italy 2009 by
Luigi Ambrosio(
Book
)
23 editions published between 2012 and 2013 in English and Undetermined and held by 136 WorldCat member libraries worldwide
In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. applied mathematicians, engineers, physicists, economists. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks and others. This book presents an extensive set of notes by world leaders on the main mathematical techniques used to address such problems, together with investigations into specific applications. The main focus is on partial differential equations in networks, but ordinary differential equations and optimal transport are also included. Moreover, the modeling is completed by analysis, numerics, control and optimization of flows in networks. The book will be a valuable resource for every researcher or student interested in the subject
23 editions published between 2012 and 2013 in English and Undetermined and held by 136 WorldCat member libraries worldwide
In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. applied mathematicians, engineers, physicists, economists. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks and others. This book presents an extensive set of notes by world leaders on the main mathematical techniques used to address such problems, together with investigations into specific applications. The main focus is on partial differential equations in networks, but ordinary differential equations and optimal transport are also included. Moreover, the modeling is completed by analysis, numerics, control and optimization of flows in networks. The book will be a valuable resource for every researcher or student interested in the subject
Transport equations and multid hyperbolic conservation laws by
Luigi Ambrosio(
Book
)
17 editions published in 2008 in English and held by 104 WorldCat member libraries worldwide
The theory of nonlinear hyperbolic equations in several space dimensions has obtained many achievements thanks to ideas and techniques related to the structure and fine properties of functions of bounded variation. This work gives an overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws
17 editions published in 2008 in English and held by 104 WorldCat member libraries worldwide
The theory of nonlinear hyperbolic equations in several space dimensions has obtained many achievements thanks to ideas and techniques related to the structure and fine properties of functions of bounded variation. This work gives an overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws
Selected papers by
Ennio De Giorgi(
Book
)
20 editions published between 2005 and 2013 in English and held by 97 WorldCat member libraries worldwide
"The book contains a selection of 43 scientific papers of the great mathematician, Ennio De Giorgi. All papers are written in English and 17 of them appear also in their original Italian version. The editors provide also a short biography of Ennio De Giorgi and a detailed account of his scientific achievements, ranging from his seminal paper on the solution of Hilbert's 19th problem to the theory of perimeter and minimal surfaces, the theory of Gconvergence and the 'Foundations of Mathematics'"Provided by publisher
20 editions published between 2005 and 2013 in English and held by 97 WorldCat member libraries worldwide
"The book contains a selection of 43 scientific papers of the great mathematician, Ennio De Giorgi. All papers are written in English and 17 of them appear also in their original Italian version. The editors provide also a short biography of Ennio De Giorgi and a detailed account of his scientific achievements, ranging from his seminal paper on the solution of Hilbert's 19th problem to the theory of perimeter and minimal surfaces, the theory of Gconvergence and the 'Foundations of Mathematics'"Provided by publisher
Variational methods for evolving objects by Variational methods for evolving objects(
Book
)
7 editions published in 2015 in English and held by 63 WorldCat member libraries worldwide
7 editions published in 2015 in English and held by 63 WorldCat member libraries worldwide
Introduction to measure theory and integration by
Luigi Ambrosio(
Book
)
14 editions published between 2011 and 2012 in English and held by 61 WorldCat member libraries worldwide
This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 20002011. The goal of the course was to present, in a quick but rigorous way, the modern point of view on measure theory and integration, putting Lebesgue's Euclidean space theory into a more general context and presenting the basic applications to Fourier series, calculus and real analysis. The text can also pave the way to more advanced courses in probability, stochastic processes or geomet
14 editions published between 2011 and 2012 in English and held by 61 WorldCat member libraries worldwide
This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 20002011. The goal of the course was to present, in a quick but rigorous way, the modern point of view on measure theory and integration, putting Lebesgue's Euclidean space theory into a more general context and presenting the basic applications to Fourier series, calculus and real analysis. The text can also pave the way to more advanced courses in probability, stochastic processes or geomet
Optimal transportation, geometry and functional inequalities by
Luigi Ambrosio(
Book
)
5 editions published in 2010 in English and held by 46 WorldCat member libraries worldwide
5 editions published in 2010 in English and held by 46 WorldCat member libraries worldwide
Geometric measure theory and real analysis by
Luigi Ambrosio(
Book
)
15 editions published between 2014 and 2015 in English and Italian and held by 24 WorldCat member libraries worldwide
In 2013, a school on Geometric Measure Theory and Real Analysis, organized by G. Alberti, C. De Lellis and myself, took place at the Centro De Giorgi in Pisa, with lectures by V. Bogachev, R. Monti, E. Spadaro and D. Vittone. The book collects the notes of the courses. The courses provide a deep and up to date insight on challenging mathematical problems and their recent developments: infinitedimensional analysis, minimal surfaces and isoperimetric problems in the Heisenberg group, regularity of subRiemannian geodesics and the regularity theory of minimal currents in any dimension and codimension
15 editions published between 2014 and 2015 in English and Italian and held by 24 WorldCat member libraries worldwide
In 2013, a school on Geometric Measure Theory and Real Analysis, organized by G. Alberti, C. De Lellis and myself, took place at the Centro De Giorgi in Pisa, with lectures by V. Bogachev, R. Monti, E. Spadaro and D. Vittone. The book collects the notes of the courses. The courses provide a deep and up to date insight on challenging mathematical problems and their recent developments: infinitedimensional analysis, minimal surfaces and isoperimetric problems in the Heisenberg group, regularity of subRiemannian geodesics and the regularity theory of minimal currents in any dimension and codimension
Corso introduttivo alla teoria geometrica della misura e alle superfici minime : appunti dei corsi tenuti da docenti della
scuola by
Luigi Ambrosio(
Book
)
7 editions published between 1996 and 1997 in Italian and held by 12 WorldCat member libraries worldwide
7 editions published between 1996 and 1997 in Italian and held by 12 WorldCat member libraries worldwide
Geometric measure theory and real analysis(
)
1 edition published in 2014 in English and held by 11 WorldCat member libraries worldwide
1 edition published in 2014 in English and held by 11 WorldCat member libraries worldwide
Scripta volant, verba manent : Ennio De Giorgi matematico e filosofo(
Book
)
3 editions published in 2008 in Italian and Undetermined and held by 11 WorldCat member libraries worldwide
3 editions published in 2008 in Italian and Undetermined and held by 11 WorldCat member libraries worldwide
Calculus of Variations and Nonlinear Partial Differential Equations With a historical overview by Elvira Mascolo by
Luigi Ambrosio(
Book
)
6 editions published in 2008 in English and held by 2 WorldCat member libraries worldwide
This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo
6 editions published in 2008 in English and held by 2 WorldCat member libraries worldwide
This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo
Biomedical composites by
Luigi Ambrosio(
Book
)
2 editions published in 2009 in English and held by 1 WorldCat member library worldwide
Biomedical composites provides a thorough review of the current status, recent progress and future trends in composites for biomedical applications
2 editions published in 2009 in English and held by 1 WorldCat member library worldwide
Biomedical composites provides a thorough review of the current status, recent progress and future trends in composites for biomedical applications
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Related Identities
 Savaré, Giuseppe Editor
 Gigli, Nicola Opponent Editor
 Centro internazionale matematico estivo Editor
 Unione matematica italiana
 Ancona, Fabio 1964 Editor
 Dacorogna, Bernard 1953 Editor
 Marcellini, Paolo Editor
 Mascolo, Elvira Collector
 Caffarelli, Luis A. Commentator Editor
 Colli, P. (Pierluigi) 1958 Editor
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Associated Subjects
Biomedical engineering Biomedical materials Boundary value problems Calculus of variations Composite materials Conservation laws (Mathematics) De Giorgi, Ennio Differential equations Differential equations, Hyperbolic Differential equations, Nonlinear Differential equations, Parabolic Differential equations, Partial Discrete groups Distribution (Probability theory) Evolution equations, Nonlinear Functional analysis Functions of bounded variation Functions of real variables Geometric analysis Geometric measure theory Geometry Geometry, Differential Global analysis (Mathematics) Global differential geometry Integrals, Generalized Interfaces (Physical sciences) Interfaces (Physical sciences)Mathematics Mathematical analysis Mathematical optimization Mathematical physics Mathematics Measure theory Metric spaces Monotone operators Reactiondiffusion equations System analysis Thermodynamics Topological degree Traffic flowMathematical models Transportation problems (Programming)
Alternative Names
Ambrosio, L.
Ambrosio, L. 1963
Ambrosio, L. (Luigi)
Ambrosio, Luigi
Luigi Ambrosio Italiaans wiskundige
Luigi Ambrosio Italian mathematician
Luigi Ambrosio italienischer Mathematiker
Luigi Ambrosio italiensk matematikar
Luigi Ambrosio italiensk matematiker
Luigi Ambrosio matemàtic italià
Luigi Ambrosio matematico e accademico italiano
Luigi Ambrosio matemático italiano
Luigi Ambrosio mathématicien italien
Луиджи Амбросио
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