Partial Differential Equations And The Calculus Of Variations
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Calculus Of Variations And Partial Differential Equations
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Author : Luigi Ambrosio
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-01-24
Calculus Of Variations And Partial Differential Equations written by Luigi Ambrosio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-24 with Mathematics categories.
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.
Differential Equations And The Calculus Of Variations
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Author : Lev Ėrnestovich Ėlʹsgolʹt︠s︡
language : en
Publisher:
Release Date : 1970
Differential Equations And The Calculus Of Variations written by Lev Ėrnestovich Ėlʹsgolʹt︠s︡ and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Calculus of variations categories.
Mathematical Problems In Image Processing
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Author : Gilles Aubert
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-30
Mathematical Problems In Image Processing written by Gilles Aubert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-30 with Mathematics categories.
Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago. Since then, intensive research has been carried out. The goals of this book are to present a variety of image analysis applications, the precise mathematics involved and how to discretize them. Thus, this book is intended for two audiences. The first is the mathematical community by showing the contribution of mathematics to this domain. It is also the occasion to highlight some unsolved theoretical questions. The second is the computer vision community by presenting a clear, self-contained and global overview of the mathematics involved in image procesing problems. This work will serve as a useful source of reference and inspiration for fellow researchers in Applied Mathematics and Computer Vision, as well as being a basis for advanced courses within these fields. During the four years since the publication of the first edition, there has been substantial progress in the range of image processing applications covered by the PDE framework. The main goals of the second edition are to update the first edition by giving a coherent account of some of the recent challenging applications, and to update the existing material. In addition, this book provides the reader with the opportunity to make his own simulations with a minimal effort. To this end, programming tools are made available, which will allow the reader to implement and test easily some classical approaches.
Variational Methods
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Author : Michael Struwe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Variational Methods written by Michael Struwe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
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.
Calculus Of Variations
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Author : Filip Rindler
language : en
Publisher: Springer
Release Date : 2018-06-20
Calculus Of Variations written by Filip Rindler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-20 with Mathematics categories.
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.
Calculus Of Variations
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Author : I. M. Gelfand
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Calculus Of Variations written by I. M. Gelfand and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.
An Introduction To Viscosity Solutions For Fully Nonlinear Pde With Applications To Calculus Of Variations In L
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Author : Nikos Katzourakis
language : en
Publisher: Springer
Release Date : 2014-11-26
An Introduction To Viscosity Solutions For Fully Nonlinear Pde With Applications To Calculus Of Variations In L written by Nikos Katzourakis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-26 with Mathematics categories.
The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE.
Partial Differential Equations And Geometric Measure Theory
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Author : Alessio Figalli
language : en
Publisher: Springer
Release Date : 2018-05-23
Partial Differential Equations And Geometric Measure Theory written by Alessio Figalli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-23 with Mathematics categories.
This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.
Multiple Integrals In The Calculus Of Variations
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Author : Charles Bradfield Morrey Jr.
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-03
Multiple Integrals In The Calculus Of Variations written by Charles Bradfield Morrey Jr. and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-03 with Mathematics categories.
From the reviews: "...the book contains a wealth of material essential to the researcher concerned with multiple integral variational problems and with elliptic partial differential equations. The book not only reports the researches of the author but also the contributions of his contemporaries in the same and related fields. The book undoubtedly will become a standard reference for researchers in these areas. ...The book is addressed mainly to mature mathematical analysts. However, any student of analysis will be greatly rewarded by a careful study of this book." M. R. Hestenes in Journal of Optimization Theory and Applications "The work intertwines in masterly fashion results of classical analysis, topology, and the theory of manifolds and thus presents a comprehensive treatise of the theory of multiple integral variational problems." L. Schmetterer in Monatshefte für Mathematik "The book is very clearly exposed and contains the last modern theory in this domain. A comprehensive bibliography ends the book." M. Coroi-Nedeleu in Revue Roumaine de Mathématiques Pures et Appliquées
Introduction To The Calculus Of Variations
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Author : Bernard Dacorogna
language : en
Publisher: World Scientific Publishing Company
Release Date : 2008-12-10
Introduction To The Calculus Of Variations written by Bernard Dacorogna and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Mathematics categories.
The calculus of variations is one of the oldest subjects in mathematics, yet is very much alive and is still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology. This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist — mathematicians, physicists, engineers, students or researchers — in discovering the subject's most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions. In this new edition, the chapter on regularity has been significantly expanded and 27 new exercises have been added. The book, containing a total of 103 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels. Request Inspection Copy Contents:PreliminariesClassical MethodsDirect Methods: ExistenceDirect Methods: RegularityMinimal SurfacesIsoperimetric InequalitySolutions to the Exercises Readership: Graduate and undergraduate students in analysis and differential equations.