Ambrosio, Luigi
Overview
Works:  75 works in 303 publications in 3 languages and 5,798 library holdings 

Genres:  Conference proceedings Textbooks 
Roles:  Author, Editor, Creator 
Classifications:  QA3, 515.42 
Publication Timeline
.
Most widely held works by
Luigi Ambrosio
Gradient flows in metric spaces and in the space of probability measures
by
Luigi Ambrosio(
)
45 editions published between 2004 and 2008 in English and German and held by 1,248 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. The two parts have some connections, due to the fact that the space of probability measures provides an important model to which the "metric" theory applies, but the book is conceived in such a way that the two parts can be read independently, the first one by the reader more interested in nonsmooth analysis and analysis in metric spaces, and the second one by the reader more orientated towards the applications in partial differential equations, measure theory and probability
45 editions published between 2004 and 2008 in English and German and held by 1,248 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. The two parts have some connections, due to the fact that the space of probability measures provides an important model to which the "metric" theory applies, but the book is conceived in such a way that the two parts can be read independently, the first one by the reader more interested in nonsmooth analysis and analysis in metric spaces, and the second one by the reader more orientated towards the applications in partial differential equations, measure theory and probability
Transport equations and multid hyperbolic conservation laws
by
Luigi Ambrosio(
)
14 editions published in 2008 in English and held by 612 WorldCat member libraries worldwide
The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements thanks to ideas and techniques related to the structure and fine properties of functions of bounded variation. This volume provides an uptodate overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws. Geometric and measure theoretic tools play a key role to obtain some fundamental advances: the wellposedness theory of linear transport equations with irregular coefficients, and the study of the BVlike structure of bounded entropy solutions to multidimensional scalar conservation laws. The volume contains surveys of recent deep results, provides an overview of further developments and related open problems, and will capture the interest of members both of the hyperbolic and the elliptic community willing to explore the intriguing interplays that link their worlds. Readers should have basic knowledge of PDE and measure theory
14 editions published in 2008 in English and held by 612 WorldCat member libraries worldwide
The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements thanks to ideas and techniques related to the structure and fine properties of functions of bounded variation. This volume provides an uptodate overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws. Geometric and measure theoretic tools play a key role to obtain some fundamental advances: the wellposedness theory of linear transport equations with irregular coefficients, and the study of the BVlike structure of bounded entropy solutions to multidimensional scalar conservation laws. The volume contains surveys of recent deep results, provides an overview of further developments and related open problems, and will capture the interest of members both of the hyperbolic and the elliptic community willing to explore the intriguing interplays that link their worlds. Readers should have basic knowledge of PDE and measure theory
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"(
)
13 editions published between 2007 and 2008 in English and held by 549 WorldCat member libraries worldwide
13 editions published between 2007 and 2008 in English and held by 549 WorldCat member libraries worldwide
Ennio De Giorgi selected papers
by
Ennio De Giorgi(
)
17 editions published between 2005 and 2013 in English and held by 447 WorldCat member libraries worldwide
Annotation
17 editions published between 2005 and 2013 in English and held by 447 WorldCat member libraries worldwide
Annotation
Optimal transportation and applications : lectures given at the C.I.M.E. summer school held in Martina Franca, Italy, September 28, 2001
by
Luigi Ambrosio(
Book
)
17 editions published in 2003 in English and held by 419 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
17 editions published in 2003 in English and held by 419 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
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
)
21 editions published in 2003 in English and held by 418 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
21 editions published in 2003 in English and held by 418 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
Nonlinear PDE's and applications C.I.M.E. Summer School, Cetraro, Italy, 2008
by
Stefano Bianchini(
)
11 editions published in 2011 in English and held by 417 WorldCat member libraries worldwide
11 editions published in 2011 in English and held by 417 WorldCat member libraries worldwide
Modelling and optimisation of flows on networks Cetraro, Italy 2009
by
Luigi Ambrosio(
)
17 editions published between 2012 and 2013 in English and Undetermined and held by 383 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
17 editions published between 2012 and 2013 in English and Undetermined and held by 383 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
Introduction to measure theory and integration
by
Luigi Ambrosio(
)
11 editions published between 2011 and 2012 in English and held by 341 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 geometric measure theory. Prerequisites for the book are a basic knowledge of calculus in one and several variables, metric spaces and linear algebra. All results presented here, as well as their proofs, are classical. The authors claim some originality only in the presentation and in the choice of the exercises. Detailed solutions to the exercises are provided in the final part of the book
11 editions published between 2011 and 2012 in English and held by 341 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 geometric measure theory. Prerequisites for the book are a basic knowledge of calculus in one and several variables, metric spaces and linear algebra. All results presented here, as well as their proofs, are classical. The authors claim some originality only in the presentation and in the choice of the exercises. Detailed solutions to the exercises are provided in the final part of the book
Functions of bounded variation and free discontinuity problems
by
Luigi Ambrosio(
Book
)
16 editions published between 2000 and 2006 in English and held by 261 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
16 editions published between 2000 and 2006 in English and held by 261 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
)
11 editions published between 1999 and 2000 in English and held by 261 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
11 editions published between 1999 and 2000 in English and held by 261 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
)
9 editions published between 2004 and 2009 in English and held by 227 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
9 editions published between 2004 and 2009 in English and held by 227 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 With a historical overview by Elvira Mascolo
by
Luigi Ambrosio(
)
4 editions published in 2008 in English and held by 38 WorldCat member libraries worldwide
4 editions published in 2008 in English and held by 38 WorldCat member libraries worldwide
Optimal transportation, geometry and functional inequalities
(
Book
)
3 editions published in 2010 in English and held by 34 WorldCat member libraries worldwide
3 editions published in 2010 in English and held by 34 WorldCat member libraries worldwide
Nonlinear PDE's and applications : CIME summer school, Cetraro, Italy, 2008
by CIME summer school(
Book
)
1 edition published in 2011 in English and held by 14 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 14 WorldCat member libraries worldwide
Corso introduttivo alla teoria geometrica della misura e alle superfici minime : appunti dei corsi tenuti da docenti della scuola
by
Luigi Ambrosio(
Book
)
6 editions published between 1996 and 1997 in Italian and held by 10 WorldCat member libraries worldwide
6 editions published between 1996 and 1997 in Italian and held by 10 WorldCat member libraries worldwide
Scripta volant, verba manent : Ennio De Giorgi matematico e filosofo
(
Book
)
4 editions published in 2008 in Italian and Undetermined and held by 9 WorldCat member libraries worldwide
4 editions published in 2008 in Italian and Undetermined and held by 9 WorldCat member libraries worldwide
Nonlinear PDE's and applications : C.I.M.E. Summer School, Cetraro, Italy 2008
(
)
1 edition published in 2011 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 8 WorldCat member libraries worldwide
Selected Topics on Analysis in Metric Spaces
by
Luigi Ambrosio(
Book
)
6 editions published in 2000 in English and Italian and held by 7 WorldCat member libraries worldwide
6 editions published in 2000 in English and Italian and held by 7 WorldCat member libraries worldwide
Lectures notes on "Analysis in metric spaces"
by
Luigi Ambrosio(
Book
)
5 editions published between 1996 and 2000 in English and held by 5 WorldCat member libraries worldwide
5 editions published between 1996 and 2000 in English and held by 5 WorldCat member libraries worldwide
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Related Identities
 Savaré, Giuseppe Editor
 Gigli, Nicola
 Centro internazionale matematico estivo Editor
 Unione matematica italiana
 Ancona, Fabio 1964 Editor
 Dacorogna, Bernard 1953 Editor
 Marcellini, Paolo Editor
 Mascolo, Elvira
 Caffarelli, Luis A. Editor
 De Giorgi, Ennio Author Editor
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Associated Subjects
Boundary value problems Calculus of variations 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 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)