Calculus Of Variations Ii

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Calculus Of Variations Ii

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Author : Mariano Giaquinta
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-30

Calculus Of Variations Ii 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 2004-06-30 with Mathematics categories.

This book by two of the foremost researchers and writers in the field is the first part of a treatise that covers the subject in breadth and depth, paying special attention to the historical origins of the theory. Both individually and collectively these volumes have already become standard references.

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.

Calculus Of Variations Ii

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Author : Mariano Giaquinta
language : en
Publisher:
Release Date : 1996

Calculus Of Variations Ii written by Mariano Giaquinta and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Calculus of variations categories.

Cartesian Currents In The Calculus Of Variations Ii

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Author : Mariano Giaquinta
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-08-19

Cartesian Currents In The Calculus Of Variations Ii 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 1998-08-19 with Mathematics categories.

This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph

Cartesian Currents In The Calculus Of Variations Ii

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Author : Mariano Giaquinta
language : en
Publisher:
Release Date : 2014-01-15

Cartesian Currents In The Calculus Of Variations Ii written by Mariano Giaquinta and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with 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 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.

Cartesian Currents In The Calculus Of Variations Ii

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Author : Mariano Giaquinta
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Cartesian Currents In The Calculus Of Variations Ii 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 2013-03-14 with Mathematics categories.

Non-scalar variational problems appear in different fields. In geometry, for in stance, we encounter the basic problems of harmonic maps between Riemannian manifolds and of minimal immersions; related questions appear in physics, for example in the classical theory of a-models. Non linear elasticity is another example in continuum mechanics, while Oseen-Frank theory of liquid crystals and Ginzburg-Landau theory of superconductivity require to treat variational problems in order to model quite complicated phenomena. Typically one is interested in finding energy minimizing representatives in homology or homotopy classes of maps, minimizers with prescribed topological singularities, topological charges, stable deformations i. e. minimizers in classes of diffeomorphisms or extremal fields. In the last two or three decades there has been growing interest, knowledge, and understanding of the general theory for this kind of problems, often referred to as geometric variational problems. Due to the lack of a regularity theory in the non scalar case, in contrast to the scalar one - or in other words to the occurrence of singularities in vector valued minimizers, often related with concentration phenomena for the energy density - and because of the particular relevance of those singularities for the problem being considered the question of singling out a weak formulation, or completely understanding the significance of various weak formulations becames non trivial.

Cartesian Currents In The Calculus Of Variations Ii

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Author : Mariano Giaquinta
language : en
Publisher:
Release Date : 1998

Cartesian Currents In The Calculus Of Variations Ii written by Mariano Giaquinta and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

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.

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.