Calculus Of Variations And Partial Differential Equations

Author : Mariano Giaquinta,Stefan Hildebrandt
Publisher : Springer Science & Business Media
Page : 512 pages
File Size : 50,6 Mb
Release : 2004-06-23
Category : Mathematics
ISBN : 354050625X

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Calculus of Variations I by Mariano Giaquinta,Stefan Hildebrandt Pdf

This two-volume treatise is a standard reference in the field. 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. It contains an introduction to each chapter, section, and subsection and an overview of the relevant literature in the footnotes and bibliography. It also includes an index of the examples used throughout the book.

Author : Luigi Ambrosio,Norman Dancer
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642571862

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Calculus of Variations and Partial Differential Equations by Luigi Ambrosio,Norman Dancer Pdf

At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

Author : Constantin Carathéodory
Publisher : Unknown
Page : 171 pages
File Size : 54,6 Mb
Release : 1965
Category : Calculus of variations
ISBN : OCLC:878090780

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Calculus of Variations and Partial Differential Equations of the First Order by Constantin Carathéodory Pdf

Author : Luigi Ambrosio,Luis A. Caffarelli,Michael G. Crandall,Lawrence C. Evans,Nicola Fusco
Publisher : Springer
Page : 213 pages
File Size : 43,9 Mb
Release : 2007-12-10
Category : Mathematics
ISBN : 9783540759140

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Calculus of Variations and Nonlinear Partial Differential Equations by Luigi Ambrosio,Luis A. Caffarelli,Michael G. Crandall,Lawrence C. Evans,Nicola Fusco Pdf

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. Coverage includes transport equations for nonsmooth vector fields, viscosity methods for the infinite Laplacian, and geometrical aspects of symmetrization.

Author : Michael Struwe
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 50,9 Mb
Release : 2013-04-17
Category : Science
ISBN : 9783662032121

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Variational Methods by Michael Struwe Pdf

Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radò. The book gives a concise introduction to variational methods and presents an overview of areas of current research in this field. This new edition has been substantially enlarged, a new chapter on the Yamabe problem has been added and the references have been updated. All topics are illustrated by carefully chosen examples, representing the current state of the art in their field.

Author : Filip Rindler
Publisher : Springer
Page : 444 pages
File Size : 41,6 Mb
Release : 2018-06-20
Category : Mathematics
ISBN : 9783319776378

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Calculus of Variations by Filip Rindler Pdf

This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether’s Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored. While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.

Author : Constantin Carathéodory
Publisher : Unknown
Page : 128 pages
File Size : 55,6 Mb
Release : 1965
Category : Calculus of variations
ISBN : LCCN:lc65024560

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Calculus of Variations and Partial Differential Equations of the First Order: Partial differential equations of the first order by Constantin Carathéodory Pdf

Author : Stefan Hildebrandt,David Kinderlehrer,Mario Miranda
Publisher : Springer
Page : 316 pages
File Size : 40,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540459323

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Calculus of Variations and Partial Differential Equations by Stefan Hildebrandt,David Kinderlehrer,Mario Miranda Pdf

Author : Irene Fonseca,Giovanni Leoni
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 50,8 Mb
Release : 2007-08-22
Category : Science
ISBN : 9780387690063

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Modern Methods in the Calculus of Variations by Irene Fonseca,Giovanni Leoni Pdf

This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.

Author : Constantin Carathéodory
Publisher : Unknown
Page : 402 pages
File Size : 45,8 Mb
Release : 1989
Category : Electronic
ISBN : LCCN:81071519

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Calculus of Variations and Partial Differential Equations of the First Order by Constantin Carathéodory Pdf

Author : Lawrence C. Evans
Publisher : American Mathematical Society
Page : 662 pages
File Size : 43,6 Mb
Release : 2022-03-22
Category : Mathematics
ISBN : 9781470469429

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Partial Differential Equations by Lawrence C. Evans Pdf

This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, a significantly expanded bibliography. About the First Edition: I have used this book for both regular PDE and topics courses. It has a wonderful combination of insight and technical detail. … Evans' book is evidence of his mastering of the field and the clarity of presentation. —Luis Caffarelli, University of Texas It is fun to teach from Evans' book. It explains many of the essential ideas and techniques of partial differential equations … Every graduate student in analysis should read it. —David Jerison, MIT I usePartial Differential Equationsto prepare my students for their Topic exam, which is a requirement before starting working on their dissertation. The book provides an excellent account of PDE's … I am very happy with the preparation it provides my students. —Carlos Kenig, University of Chicago Evans' book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge … An outstanding reference for many aspects of the field. —Rafe Mazzeo, Stanford University

Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 43,6 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567

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Partial Differential Equations by Walter A. Strauss Pdf

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Author : Stefan Hildebrandt,Rolf Leis
Publisher : Springer
Page : 433 pages
File Size : 46,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540460244

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Partial Differential Equations and Calculus of Variations by Stefan Hildebrandt,Rolf Leis Pdf

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.

Author : Luigi Ambrosio,Alessandro Carlotto,Annalisa Massaccesi
Publisher : Springer
Page : 230 pages
File Size : 51,5 Mb
Release : 2019-01-10
Category : Mathematics
ISBN : 9788876426513

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Lectures on Elliptic Partial Differential Equations by Luigi Ambrosio,Alessandro Carlotto,Annalisa Massaccesi Pdf

The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.

Author : Mariano Giaquinta,Stefan Hildebrandt
Publisher : Springer Science & Business Media
Page : 498 pages
File Size : 54,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662032787

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Calculus of Variations I by Mariano Giaquinta,Stefan Hildebrandt Pdf

This two-volume treatise is a standard reference in the field. 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. It contains an introduction to each chapter, section, and subsection and an overview of the relevant literature in the footnotes and bibliography. It also includes an index of the examples used throughout the book.