Partial Differential Equations And Calculus Of Variations

Author : Luigi Ambrosio,Norman Dancer
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642571862

Get Book

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 : Gilles Aubert,Pierre Kornprobst
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 40,6 Mb
Release : 2008-04-06
Category : Mathematics
ISBN : 9780387217666

Get Book

Mathematical Problems in Image Processing by Gilles Aubert,Pierre Kornprobst Pdf

Partial differential equations and variational methods were introduced into image processing about 15 years ago, and intensive research has been carried out since then. The main goal of this work is to present the variety of image analysis applications and the precise mathematics involved. It is intended for two audiences. The first is the mathematical community, to show the contribution of mathematics to this domain and to highlight some unresolved theoretical questions. The second is the computer vision community, to present a clear, self-contained, and global overview of the mathematics involved in image processing problems. The book is divided into five main parts. Chapter 1 is a detailed overview. Chapter 2 describes and illustrates most of the mathematical notions found throughout the work. Chapters 3 and 4 examine how PDEs and variational methods can be successfully applied in image restoration and segmentation processes. Chapter 5, which is more applied, describes some challenging computer vision problems, such as sequence analysis or classification. This book will be useful to researchers and graduate students in mathematics and computer vision.

Author : Stefan Hildebrandt,Rolf Leis
Publisher : Springer
Page : 433 pages
File Size : 48,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540460244

Get Book

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 : COLOMBINI,MARINO,MODICA,SPAGNOLA
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 49,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781461598312

Get Book

Partial Differential Equations and the Calculus of Variations by COLOMBINI,MARINO,MODICA,SPAGNOLA Pdf

The Italian school of Mathematical Analysis has long and glo rious traditions. In the last thirty years it owes very much to the scientific pre-eminence of Ennio De Giorgi, Professor of Mathemati cal Analysis at the Scuola Normale Superiore di Pisa. His fundamental theorems in Calculus of Variations, in Minimal Surfaces Theory, in Partial Differential Equations, in Axiomatic Set Theory as well as the fertility of his mind to discover both general mathematical structures and techniques which frame many different problems, and profound and meaningful examples which show the limits of a theory and give origin to new results and theories, makes him an absolute reference point for all Italian mathematicians, and a well-known and valued personage in the international mathematical world. We have been students of Ennio de Giorgi. Now, we are glad to present to him, together with all his collegues, friends and former students, these Essays of Mathematical Analysis written in his hon our on the occasion of his sixtieth birthday (February 8th, 1988), with our best wishes and our thanks for all he gave in the past and will give us in the future. We have added to the research papers of this book the text of a conversation with Ennio De Giorgi about the diffusion and the communication of science and, in particular, of Mathematics.

Author : Luigi Ambrosio,Luis A. Caffarelli,Michael G. Crandall,Lawrence C. Evans,Nicola Fusco
Publisher : Springer
Page : 213 pages
File Size : 49,8 Mb
Release : 2007-12-10
Category : Mathematics
ISBN : 9783540759140

Get Book

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 : Enrico Giusti
Publisher : World Scientific
Page : 412 pages
File Size : 42,6 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812380432

Get Book

Direct Methods in the Calculus of Variations by Enrico Giusti Pdf

This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well known and have been widely used in the last century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this book, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory.

Author : Constantin Carathéodory
Publisher : Unknown
Page : 402 pages
File Size : 40,7 Mb
Release : 1989
Category : Electronic
ISBN : LCCN:81071519

Get Book

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

Author : Luigi Ambrosio,E. Mascolo
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 42,7 Mb
Release : 2008-01-02
Category : Mathematics
ISBN : 9783540759133

Get Book

Calculus of Variations and Nonlinear Partial Differential Equations by Luigi Ambrosio,E. Mascolo Pdf

With a historical overview by Elvira Mascolo

Author : Michael Struwe
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 53,6 Mb
Release : 2013-04-17
Category : Science
ISBN : 9783662032121

Get Book

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 : Stefan Hildebrandt,David Kinderlehrer,Mario Miranda
Publisher : Springer
Page : 316 pages
File Size : 48,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540459323

Get Book

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

Author : Lev Elsgolts
Publisher : Unknown
Page : 444 pages
File Size : 41,8 Mb
Release : 2003-12-01
Category : Mathematics
ISBN : 1410210677

Get Book

Differential Equations and the Calculus of Variations by Lev Elsgolts Pdf

Originally published in the Soviet Union, this text is meant for students of higher schools and deals with the most important sections of mathematics - differential equations and the calculus of variations. The first part describes the theory of differential equations and reviews the methods for integrating these equations and investigating their solutions. The second part gives an idea of the calculus of variations and surveys the methods for solving variational problems. The book contains a large number of examples and problems with solutions involving applications of mathematics to physics and mechanics. Apart from its main purpose the textbook is of interest to expert mathematicians. Lev Elsgolts (deceased) was a Doctor of Physico-Mathematical Sciences, Professor at the Patrice Lumumba University of Friendship of Peoples. His research work was dedicated to the calculus of variations and differential equations. He worked out the theory of differential equations with deviating arguments and supplied methods for their solution. Lev Elsgolts was the author of many printed works. Among others, he wrote the well-known books Qualitative Methods in Mathematical Analysis and Introduction to the Theory of Differential Equations with Deviating Arguments. In addition to his research work Lev Elsgolts taught at higher schools for over twenty years.

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

Get Book

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

Author : COLOMBINI,MARINO,MODICA,SPAGNOLA
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461598282

Get Book

Partial Differential Equations and the Calculus of Variations by COLOMBINI,MARINO,MODICA,SPAGNOLA Pdf

The Italian school of Mathematical Analysis has long and glo rious traditions. In the last thirty years it owes very much to the scientific pre-eminence of Ennio De Giorgi, Professor of Mathemati cal Analysis at the Scuola Normale Superiore di Pisa. His fundamental theorems in Calculus of Variations, in Minimal Surfaces Theory, in Partial Differential Equations, in Axiomatic Set Theory as well as the fertility of his mind to discover both general mathematical structures and techniques which frame many different problems, and profound and meaningful examples which show the limits of a theory and give origin to new results and theories, makes him an absolute reference point for all Italian mathematicians, and a well-known and valued personage in the international mathematical world. We have been students of Ennio de Giorgi. Now, we are glad to present to him, together with all his collegues, friends and former students, these Essays of Mathematical Analysis written in his hon our on the occasion of his sixtieth birthday (February 8th, 1988), with our best wishes and our thanks for all he gave in the past and will give us in the future. We have added to the research papers of this book the text of a conversation with Ennio De Giorgi about the diffusion and the communication of science and, in particular, of Mathematics.

Author : John A. Burns
Publisher : CRC Press
Page : 562 pages
File Size : 45,5 Mb
Release : 2013-08-28
Category : Mathematics
ISBN : 9781466571402

Get Book

Introduction to the Calculus of Variations and Control with Modern Applications by John A. Burns Pdf

Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions a

Author : Michael Struwe
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783662041949

Get Book

Variational Methods by Michael Struwe Pdf

Hilberts 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 Plateaus problem by Douglas and Rad. This third edition gives a concise introduction to variational methods and presents an overview of areas of current research in the field, plus a survey on new developments.