Modern Methods in the Calculus of Variations: L^p Spaces / Edition 1

Modern Methods in the Calculus of Variations: L^p Spaces / Edition 1

by Irene Fonseca, Giovanni Leoni
     
 

ISBN-10: 1441922601

ISBN-13: 9781441922601

Pub. Date: 11/29/2010

Publisher: Springer New York

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

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Overview

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.

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Product Details

ISBN-13:
9781441922601
Publisher:
Springer New York
Publication date:
11/29/2010
Series:
Springer Monographs in Mathematics Series
Edition description:
Softcover reprint of hardcover 1st ed. 2007
Pages:
600
Product dimensions:
1.25(w) x 6.14(h) x 9.21(d)

Table of Contents

Measure Theory and Lp Spaces.- Measures.- Lp Spaces.- The Direct Method and Lower Semicontinuity.- The Direct Method and Lower Semicontinuity.- ConvexAnalysis.- Functionals Defined on Lp.- Integrands f = f (z).- Integrands f = f (x, z).- Integrands f = f (x, u, z).- Young Measures.

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