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

by Irene Fonseca, Giovanni Leoni

Overview

This book is a unified presentation of both classical and contemporary results in the calculus of variations. It offers a comprehensive analysis of necessary and sufficient conditions for sequential lower semicontinuity of functionals on Lp spaces, followed by relaxation techniques. In recent years there has been a remarkable and renewed interest in this area, motivated in part by applications of allied disciplines. Based on a series of lectures by Irene Fonseca at Carnegie Mellon University, this book was written in response to the need to bring together in one volume contemporary developments in the calculus of variations. Because it is largely self-contained, the book will appeal to non-specialists and new students in this discipline. It is intended for use as a graduate text and as a reference for more experienced researchers working in the area.

Product Details

ISBN-13:	9781441922601
Publisher:	Springer New York
Publication date:	11/29/2010
Series:	Springer Monographs in Mathematics
Edition description:	Softcover reprint of hardcover 1st ed. 2007
Pages:	600
Product dimensions:	6.10(w) x 9.25(h) x 0.36(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.

Editorial Reviews

From the reviews:

"This book is intended as a graduate textbook and reference for those who work in the modern calculus of variations. … interesting examples and exercises help to keep the reader on track. Several open problems are indicated as well. … excellent presentation." (Erik J. Balder, Mathematical Reviews, Issue 2008 m)

"This book is the first of two volumes in the calculus of variations and measure theory. The main objective of this book is to introduce necessary and sufficient conditions for sequential lower semicontinuity of functionals on L^p-spaces. … This book is very nicely written, self-contained and it is an excellent and modern introduction to the calculus of variations." (Jean-Pierre Raymond, Zentrablatt MATH, Vol. 1153, 2009)

“This is the first of a two-volume introduction into direct methods in the calculus of variations. Its main topic is the analysis of necessary and sufficient conditions for lower semicontinuity on L^p-spaces, as well as of relaxation techniques. … The book provides a well-written and self-contained introduction to an active area of research and will be valuable both to graduate students as an introduction and to researchers in the field as a reference work.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 156 (4), April, 2009)

From the Publisher