Direct Methods In The Calculus Of Variations
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Direct Methods In The Calculus Of Variations
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Author : Enrico Giusti
language : en
Publisher: World Scientific
Release Date : 2003
Direct Methods In The Calculus Of Variations written by Enrico Giusti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
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.
Direct Methods In The Calculus Of Variations
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Author : Bernard Dacorogna
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-21
Direct Methods In The Calculus Of Variations written by Bernard Dacorogna 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 2007-11-21 with Mathematics categories.
This book is developed for the study of vectorial problems in the calculus of variations. The subject is a very active one and almost half of the book consists of new material. This is a new edition of the earlier book published in 1989 and it is suitable for graduate students. The book has been updated with some new material and examples added. Applications are included.
Calculus Of Variations
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Author : Izrailʹ Moiseevich Gelʹfand
language : en
Publisher: Prentice Hall
Release Date : 1963
Calculus Of Variations written by Izrailʹ Moiseevich Gelʹfand and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Mathematics categories.
Elements of the theory -- Further generalizations -- The general variation of a functional -- The canonical form of the euler equations and related topics -- The second variation : sufficient conditions for a weak extremum -- Fields : sufficient conditions for a strong extremum -- Variational problems involving multiple integrals -- Direct methods in the calculus of variations -- Appendix I. Propagation of disturbances and the canonical equations -- Appendix II. Variational methods in problems of optimal control.
Computational Methods In The Fractional Calculus Of Variations
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Author : Ricardo Almeida
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-03-19
Computational Methods In The Fractional Calculus Of Variations written by Ricardo Almeida 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 2015-03-19 with Mathematics categories.
This book fills a gap in the literature by introducing numerical techniques to solve problems of fractional calculus of variations (FCV). In most cases, finding the analytic solution to such problems is extremely difficult or even impossible, and numerical methods need to be used.The authors are well-known researchers in the area of FCV and the book contains some of their recent results, serving as a companion volume to Introduction to the Fractional Calculus of Variations by A B Malinowska and D F M Torres, where analytical methods are presented to solve FCV problems. After some preliminaries on the subject, different techniques are presented in detail with numerous examples to help the reader to better understand the methods. The techniques presented may be used not only to deal with FCV problems but also in other contexts of fractional calculus, such as fractional differential equations and fractional optimal control. It is suitable as an advanced book for graduate students in mathematics, physics and engineering, as well as for researchers interested in fractional calculus.
Modern Methods In The Calculus Of Variations
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Author : Irene Fonseca
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-22
Modern Methods In The Calculus Of Variations written by Irene Fonseca 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 2007-08-22 with Science categories.
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.
The Calculus Of Variations
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Author : N.I. Akhiezer
language : en
Publisher: CRC Press
Release Date : 1988-01-01
The Calculus Of Variations written by N.I. Akhiezer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
An authoritative text on the calculus of variations for first-year graduate students. From a study of the simplest problem it goes on to cover Lagrangian derivatives, Jacobi’s condition, and field theory. Devotes considerable attention to direct methods and the Sturm-Liouville problem in a finite interval. Contains numerous interesting and challenging exercises plus five appendices on important results, generalizations, and applications of the material,
Calculus Of Variations
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Author : L. E. Elsgolc
language : en
Publisher: Elsevier
Release Date : 2014-07-10
Calculus Of Variations written by L. E. Elsgolc and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter is illustrated by a large number of problems some of which are taken from existing textbooks. The solutions to the problems in each chapter are provided at the end of the book.
Introduction To The Calculus Of Variations
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Author : U. Brechteken-Mandersch
language : en
Publisher: CRC Press
Release Date : 1991-06-01
Introduction To The Calculus Of Variations written by U. Brechteken-Mandersch and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-06-01 with Mathematics categories.
This text provides a clear, concise introduction to the calculus of variations. The introductory chapter provides a general sense of the subject through a discussion of several classical and contemporary examples of the subject's use.
Direct Methods In The Calculus Of Variations
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Author : Bernard Dacorogna
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Direct Methods In The Calculus Of Variations written by Bernard Dacorogna 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 2012-12-06 with Mathematics categories.
In recent years there has been a considerable renewal of interest in the clas sical problems of the calculus of variations, both from the point of view of mathematics and of applications. Some of the most powerful tools for proving existence of minima for such problems are known as direct methods. They are often the only available ones, particularly for vectorial problems. It is the aim of this book to present them. These methods were introduced by Tonelli, following earlier work of Hilbert and Lebesgue. Although there are excellent books on calculus of variations and on direct methods, there are recent important developments which cannot be found in these books; in particular, those dealing with vector valued functions and relaxation of non convex problems. These two last ones are important in appli cations to nonlinear elasticity, optimal design . . . . In these fields the variational methods are particularly effective. Part of the mathematical developments and of the renewal of interest in these methods finds its motivations in nonlinear elasticity. Moreover, one of the recent important contributions to nonlinear analysis has been the study of the behaviour of nonlinear functionals un der various types of convergence, particularly the weak convergence. Two well studied theories have now been developed, namely f-convergence and compen sated compactness. They both include as a particular case the direct methods of the calculus of variations, but they are also, both, inspired and have as main examples these direct methods.
Lecture Notes On Calculus Of Variations
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Author : Kung Ching Chang
language : en
Publisher: World Scientific
Release Date : 2016-09-16
Lecture Notes On Calculus Of Variations written by Kung Ching Chang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-16 with Mathematics categories.
This is based on the course "Calculus of Variations" taught at Peking University from 2006 to 2010 for advanced undergraduate to graduate students majoring in mathematics. The book contains 20 lectures covering both the theoretical background material as well as an abundant collection of applications. Lectures 1–8 focus on the classical theory of calculus of variations. Lectures 9–14 introduce direct methods along with their theoretical foundations. Lectures 15–20 showcase a broad collection of applications. The book offers a panoramic view of the very important topic on calculus of variations. This is a valuable resource not only to mathematicians, but also to those students in engineering, economics, and management, etc.