Contributions To Modern Calculus Of Variations
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Contributions To Modern Calculus Of Variations
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Author : Lamberto Cesari
language : en
Publisher: Longman
Release Date : 1987
Contributions To Modern Calculus Of Variations written by Lamberto Cesari and has been published by Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
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.
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
The Calculus Of Variations And Functional Analysis
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Author : L. P. Lebedev
language : en
Publisher: World Scientific
Release Date : 2003
The Calculus Of Variations And Functional Analysis written by L. P. Lebedev 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.
In this book, Sam helps his goose sisters fly to safety to looking for familiar landforms.
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.
The Interaction Of Analysis And Geometry
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Author : Victor I. Burenkov
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
The Interaction Of Analysis And Geometry written by Victor I. Burenkov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Based on talks given at the International Conference on Analysis and Geometry in honor of the 75th birthday of Yurii Reshetnyak (Novosibirsk, 2004), this title includes topics such as geometry of spaces with bounded curvature in the sense of Alexandrov, quasiconformal mappings and mappings with bounded distortion, and nonlinear potential theory."
One Dimensional Variational Problems
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Author : Giuseppe Buttazzo
language : en
Publisher: Oxford University Press
Release Date : 1998
One Dimensional Variational Problems written by Giuseppe Buttazzo and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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.
The Calculus Of Variations In The Large
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Author : Marston Morse
language : en
Publisher: American Mathematical Soc.
Release Date : 1934-12-31
The Calculus Of Variations In The Large written by Marston Morse and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1934-12-31 with Mathematics categories.
Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calculus of Variations in the Large is certainly one of the essential references on Morse theory.
Linear And Nonlinear Functional Analysis With Applications Second Edition
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Author : Philippe G. Ciarlet
language : en
Publisher: SIAM
Release Date : 2025-04-23
Linear And Nonlinear Functional Analysis With Applications Second Edition written by Philippe G. Ciarlet and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-23 with Mathematics categories.
This new, considerably expanded edition covers the fundamentals of linear and nonlinear functional analysis, including distribution theory, harmonic analysis, differential geometry, calculus of variations, and degree theory. Numerous applications are included, especially to linear and nonlinear partial differential equations and to numerical analysis. All the basic theorems are provided with complete and detailed proofs. The author has added more than 450 pages of new material; added more than 210 problems; the solutions to all of the problems will be made available on an accompanying website; added two entirely new chapters, one on locally convex spaces and distribution theory and the other on the Fourier transform and Calderón–Zygmund singular integral operators; and enlarged and split the chapter on the “great theorems” of nonlinear functional analysis into two chapters, one on the calculus of variations and the other on Brouwer’s theorem, Brouwer’s degree, and Leray–Schauder’s degree. Ideal for both teaching and self-study, Linear and Nonlinear Functional Analysis with Applications, Second Edition is intended for advanced undergraduate and graduate students in mathematics, university professors, and researchers. It is also an ideal basis for several courses on linear or nonlinear functional analysis.
Calculus Of Variations I
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Author : Mariano Giaquinta
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-23
Calculus Of Variations I written by Mariano Giaquinta 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 2004-06-23 with Mathematics categories.
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.