WorldCat Identities

Hildebrandt, Stefan

Overview
Works: 172 works in 631 publications in 5 languages and 8,209 library holdings
Genres: Conference papers and proceedings  History 
Roles: Author, Editor, Honoree, Other, Contributor
Classifications: BH301.N3, 117
Publication Timeline
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Most widely held works by Stefan Hildebrandt
Mathematics and optimal form by Stefan Hildebrandt( Book )

30 editions published between 1984 and 1998 in 4 languages and held by 1,451 WorldCat member libraries worldwide

The authors look at familiar examples of nature's tendency to economize, to the nuclei of atoms to the planets of our solar system
The parsimonious universe : shape and form in the natural world by Stefan Hildebrandt( Book )

20 editions published between 1995 and 2013 in English and German and held by 767 WorldCat member libraries worldwide

Can one set of basic laws account for both the recurring themes and the infinite variety of nature's designs? When it comes to shape and form, does nature simply proceed in the easiest, most efficient way? Complete answers to these questions are likely never to be discovered. Still, down through the ages, the investigation of symmetry and regularity in nature has yielded some fascinating and surprising insights. Out of this inquiry comes a specific branch of mathematics - the calculus of variations - which explores questions of optimization: Is the igloo the optimal housing form for minimizing heat loss? Do bees use the least possible amount of wax when building their hives? In The Parsimonious Universe, Stefan Hildebrandt and Anthony Tromba invite readers to join the search for the mathematical underpinnings of natural shapes and form. Moving from ancient times to the nuclear age, the book looks at centuries of evidence that the physical world adheres to the principle of the economy of means - meaning that nature achieves efficiency by being rather stingy with the energy it expends. On almost every page can be found historical discussions, striking color illustrations, and examples ranging from atomic nuclei to soap bubbles to spirals and fractals. Without using technical language, Hildebrandt and Tromba open up an intriguing avenue of scientific inquiry to an uninitiated readership, showing what can be discovered when mathematics is used to investigate the natural world
Calculus of variations by Mariano Giaquinta( Book )

43 editions published between 1995 and 2011 in English and Undetermined and held by 484 WorldCat member libraries worldwide

This long-awaited book by two of the foremost researchers and writers in the field is the first part of a treatise that covers the subject in breadth and depth, paying special attention to the historical origins, partly in applications, e.g. from geometrical optics, of parts of the theory. A variety of aids to the reader are provided: besides the very detailed table of contents, an introduction to each chapter, section and subsection, an overview of the relevant literature (in Vol. 2) plus the references in the Scholia to each chapter, in the (historical) footnotes, and in the bibliography, and finally an index of the examples used throughout the book. Both individually and collectively these volumes have already become standard references
Calculus of variations and partial differential equations : proceedings of a conference held in Trento, Italy, June 16-21, 1986 by Stefan Hildebrandt( Book )

18 editions published in 1988 in English and held by 389 WorldCat member libraries worldwide

Partial differential equations and calculus of variations by Stefan Hildebrandt( Book )

18 editions published in 1988 in English and Undetermined and held by 387 WorldCat member libraries worldwide

This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory
Calculus of variations and geometric evolution problems : lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 15-22, 1996 by Fabrice Bethuel( Book )

27 editions published in 1999 in English and German and held by 337 WorldCat member libraries worldwide

The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory
One-dimensional variational problems : an introduction by Giuseppe Buttazzo( Book )

15 editions published between 1998 and 2010 in English and Russian and held by 282 WorldCat member libraries worldwide

While easier to solve and accessible to a broader range of students, one-dimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higher-dimensional problems. This book, the first moden introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory
Geometric analysis and nonlinear partial differential equations by Stefan Hildebrandt( Book )

12 editions published between 2002 and 2013 in English and held by 212 WorldCat member libraries worldwide

This well-organized and coherent collection of papers leads the reader to the frontiers of present research in the theory of nonlinear partial differential equations and the calculus of variations and offers insight into some exciting developments. In addition, most articles also provide an excellent introduction to their background, describing extensively as they do the history of those problems presented, as well as the state of the art and offer a well-chosen guide to the literature. Part I contains the contributions of geometric nature: From spectral theory on regular and singular spaces to regularity theory of solutions of variational problems. Part II consists of articles on partial differential equations which originate from problems in physics, biology and stochastics. They cover elliptic, hyperbolic and parabolic cases
Wahrheit und Wert mathematischer Erkenntnis : Vortrag gehalten in der Carl Friedrich von Siemens Stiftung am 6. Februar 1992 by Stefan Hildebrandt( Book )

13 editions published in 1995 in German and held by 157 WorldCat member libraries worldwide

Minimal surfaces by Ulrich Dierkes( Book )

22 editions published between 2010 and 2013 in English and held by 141 WorldCat member libraries worldwide

"Minimal Surfaces" is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339-341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise is a substantially revised and extended version of the monograph Minimal Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume begins with an exposition of basic ideas of the theory of surfaces in three-dimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently
Regularity of minimal surfaces by Ulrich Dierkes( Book )

19 editions published between 2010 and 2013 in English and held by 138 WorldCat member libraries worldwide

"Regularity of Minimal Surfaces" begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general Gauss-Bonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is t
Global analysis of minimal surfaces by Ulrich Dierkes( Book )

21 editions published between 2010 and 2013 in English and held by 131 WorldCat member libraries worldwide

Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with partially free boundaries. Here one of the main features is the possibility of 'edge-crawling' along free parts of the boundary. The third chapter deals with a priori estimates for minimal surfaces in higher dimensions and for minimizers of singular integrals related to the area functional. In particular, far reaching Bernstein theorems are derived. The second part of the book contains what one might justly call a 'global theory of minimal surfaces' as envisioned by Smale. First, the Douglas problem is treated anew by using Teichmuller theory. Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateau's problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented
Analysis by Stefan Hildebrandt( Book )

9 editions published between 2002 and 2006 in German and English and held by 116 WorldCat member libraries worldwide

Calculus of variations : mit besonderer Berücksichtigung der Anwendungsgebiete by Mariano Giaquinta( Book )

30 editions published between 1994 and 2010 in English and held by 115 WorldCat member libraries worldwide

This 2-volume treatise by two of the leading researchers and writers in the field, quickly established itself as a standard reference. It pays special attention to the historical aspects and the origins partly in applied problems - such as those of geometric optics - of parts of the theory. A variety of aids to the reader are provided, beginning with the detailed table of contents, and including an introduction to each chapter and each section and subsection, an overview of the relevant literature (in Volume II) besides the references in the Scholia to each chapter in the (historical) footnotes, and in the bibliography, and finally an index of the examples used through out the book
Geometric analysis and the calculus of variations : for Stefan Hildebrandt( Book )

9 editions published in 1996 in English and held by 87 WorldCat member libraries worldwide

Otto Toeplitz by Stefan Hildebrandt( Book )

9 editions published between 1950 and 1999 in German and English and held by 57 WorldCat member libraries worldwide

Presents a brief biographical sketch of Jewish German mathematician Otto Toeplitz (1881-1940), compiled as part of the MacTutor History of Mathematics Archive of the School of Mathematics and Statistics at the University of Saint Andrews in Scotland. Notes that Toeplitz's work focused on infinite linear and quadratic forms
On one-to-one harmonic mappings and minimal surfaces by Stefan Hildebrandt( Book )

6 editions published between 1991 and 1992 in English and German and held by 57 WorldCat member libraries worldwide

Analysis 2 by Stefan Hildebrandt( Book )

6 editions published between 2002 and 2008 in German and held by 38 WorldCat member libraries worldwide

Der zweite Band dieses Lehrbuchs der Analysis umfaßt den Stoff des zweiten Semesters eines mathematischen Grundstudiums für Studierende der Mathematik, Physik und Informatik. Der klare und übersichtliche Aufbau berücksichtigt, daß schon frühzeitig die mathematischen Hilfsmittel erörtert werden, die zum Verständnis der physikalischen Grundvorlesungen unerläßlich sind. In Verbindung mit Band 1 ist so ein Leitfaden für das Studium der Analysis entstanden, der das in den ersten beiden Studiensemestern zu erwerbende mathematische Grundwissen umfaßt. Ausführliche Beweise und Erläuterungen sowie zahlreiche Beispiele und interessante Übungsaufgaben eignen es sehr gut für das Selbststudium. Ein klarer und übersichtlicher Aufbau und eine geschickte Gliederung des Stoffes ermöglichen, das erste Studium auf Kernbereiche zu beschränken. Geometrische Intuition und historische Motivation in Verbindung mit einer maßvollen Abstraktion kennzeichnen diese moderne Einführung in die Analysis
Nonlinear problems in mathematical physics and related topics : in honor of Professor O.A. Ladyzhenskaya by M. Sh Birman( Book )

3 editions published in 2002 in English and held by 5 WorldCat member libraries worldwide

The new series, International Mathematical Series founded by Kluwer / Plenum Publishers and the Russian publisher, Tamara Rozhkovskaya is published simultaneously in English and in Russian and starts with two volumes dedicated to the famous Russian mathematician Professor Olga Aleksandrovna Ladyzhenskaya, on the occasion of her 80th birthday. O.A. Ladyzhenskaya graduated from the Moscow State University. But throughout her career she has been closely connected with St. Petersburg where she works at the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences. Many generations of mathematicians have become familiar with the nonlinear theory of partial differential equations reading the books on quasilinear elliptic and parabolic equations written by O.A. Ladyzhenskaya with V.A. Solonnikov and N.N. Uraltseva. Her results and methods on the Navier-Stokes equations, and other mathematical problems in the theory of viscous fluids, nonlinear partial differential equations and systems, the regularity theory, some directions of computational analysis are well known. So it is no surprise that these two volumes attracted leading specialists in partial differential equations and mathematical physics from more than 15 countries, who present their new results in the various fields of mathematics in which the results, methods, and ideas of O.A. Ladyzhenskaya played a fundamental role. Nonlinear Problems in Mathematical Physics and Related Topics I presents new results from distinguished specialists in the theory of partial differential equations and analysis. A large part of the material is devoted to the Navier-Stokes equations, which play an important role in the theory of viscous fluids. In particular, the existence of a local strong solution (in the sense of Ladyzhenskaya) to the problem describing some special motion in a Navier-Stokes fluid is established. Ladyzhenskaya's results on axially symmetric solutions to the Navier-Stokes fluid are generalized and solutions with fast decay of nonstationary Navier-Stokes equations in the half-space are stated. Application of the Fourier-analysis to the study of the Stokes wave problem and some interesting properties of the Stokes problem are presented. The nonstationary Stokes problem is also investigated in nonconvex domains and some Lp-estimates for the first-order derivatives of solutions are obtained. New results in the theory of fully nonlinear equations are presented. Some asymptotics are derived for elliptic operators with strongly degenerated symbols. New results are also presented for variational problems connected with phase transitions of means in controllable dynamical systems, nonlocal problems for quasilinear parabolic equations, elliptic variational problems with nonstandard growth, and some sufficient conditions for the regularity of lateral boundary. Additionally, new results are presented on area formulas, estimates for eigenvalues in the case of the weighted Laplacian on Metric graph, application of the direct Lyapunov method in continuum mechanics, singular perturbation property of capillary surfaces, partially free boundary problem for parametric double integrals
Felix Hausdorff Gesammelte Werke by Josef Bemelmans( )

2 editions published in 2006 in German and held by 0 WorldCat member libraries worldwide

Band 5 umfabt die Themenbereiche Astronomie, Optik und Wahrscheinlichkeitstheorie. Er enthalt Hausdorffs Dissertation uber die Refraktion des Lichtes in der Atmosphare, zwei Folgearbeiten zum gleichen Thema sowie die Habilitationsschrift uber die Extinktion des Lichtes in der Atmosphare. Es folgt eine Arbeit uber geometrische Optik
 
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The parsimonious universe : shape and form in the natural world
Alternative Names
Hildebrandt, S.

Hildebrandt, S. 1936-2015

Hildebrandt, S. (Stefan)

Hildebrandt, St. 1936-2015

Hildebrandt, Stefan

Hildebrandt, Stefan O. W.

Hildebrandt, Stephan 1936-

Hildebrandt, Stephan 1936-2015

Hilderbrandt, S.

Hilderbrandt, S. (Stefan)

Stefan Hildebrandt deutscher Mathematiker

Stefan Hildebrandt Duits wiskundige (1936-2015)

Stefan Hildebrandt German mathematician

Stefan Hildebrandt tysk matematikar

Stefan Hildebrandt tysk matematiker

Languages
English (272)

German (47)

French (6)

Japanese (3)

Russian (1)

Covers
Calculus of variationsCalculus of variations and partial differential equations : proceedings of a conference held in Trento, Italy, June 16-21, 1986Partial differential equations and calculus of variationsCalculus of variations and geometric evolution problems : lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 15-22, 1996One-dimensional variational problems : an introductionGeometric analysis and nonlinear partial differential equationsMinimal surfacesRegularity of minimal surfaces