Bibliography For The Theory Of Multiple Integrals In The Calculus Of Variations
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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
Bibliography For The Theory Of Multiple Integrals In The Calculus Of Variations
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Author :
language : en
Publisher:
Release Date : 1942
Bibliography For The Theory Of Multiple Integrals In The Calculus Of Variations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1942 with Calculus of variations categories.
Calculus Of Variations With Applications
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Author : George McNaught Ewing
language : en
Publisher: Courier Corporation
Release Date : 1985-01-01
Calculus Of Variations With Applications written by George McNaught Ewing and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Mathematics categories.
Applications-oriented introduction to variational theory develops insight and promotes understanding of specialized books and research papers. Suitable for advanced undergraduate and graduate students as a primary or supplementary text. 1969 edition.
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.
The American Mathematical Monthly
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Author :
language : en
Publisher:
Release Date : 1983
The American Mathematical Monthly written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematicians categories.
Calculus Of Variations I
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Author : Mariano Giaquinta
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
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 2013-03-09 with Mathematics categories.
This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deals with the for mal apparatus of the variational calculus and with nonparametric field theory, whereas Volume 2 treats parametric variational problems as well as Hamilton Jacobi theory and the classical theory of partial differential equations of first ordel;. In a subsequent treatise we shall describe developments arising from Hilbert's 19th and 20th problems, especially direct methods and regularity theory. Of the classical variational calculus we have particularly emphasized the often neglected theory of inner variations, i. e. of variations of the independent variables, which is a source of useful information such as mono tonicity for mulas, conformality relations and conservation laws. The combined variation of dependent and independent variables leads to the general conservation laws of Emmy Noether, an important tool in exploiting symmetries. Other parts of this volume deal with Legendre-Jacobi theory and with field theories. In particular we give a detailed presentation of one-dimensional field theory for nonpara metric and parametric integrals and its relations to Hamilton-Jacobi theory, geometrical optics and point mechanics. Moreover we discuss various ways of exploiting the notion of convexity in the calculus of variations, and field theory is certainly the most subtle method to make use of convexity. We also stress the usefulness of the concept of a null Lagrangian which plays an important role in we give an exposition of Hamilton-Jacobi several instances.
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Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
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.
Minimal Surfaces I
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Author : Ulrich Dierkes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Minimal Surfaces I written by Ulrich Dierkes 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 2013-11-27 with Mathematics categories.
Minimal surfaces I is an introduction to the field of minimal surfaces and apresentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can alsobe useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory fornonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.
The Hodge Laplacian
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Author : Dorina Mitrea
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-01-27
The Hodge Laplacian written by Dorina Mitrea and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-27 with Mathematics categories.
The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains. The 1-st edition of the “Hodge-Laplacian”, De Gruyter Studies in Mathematics, Volume 64, 2016, is a trailblazer of its kind, having been written at a time when new results in Geometric Measure Theory have just emerged, or were still being developed. In particular, this monograph is heavily reliant on the bibliographical items. The latter was at the time an unpublished manuscript which eventually developed into the five-volume series “Geometric Harmonic Analysis” published by Springer 2022-2023. The progress registered on this occasion greatly impacts the contents of the “Hodge-Laplacian” and warrants revisiting this monograph in order to significantly sharpen and expand on previous results. This also allows us to provide specific bibliographical references to external work invoked in the new edition. Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals.