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Modern Methods in the Calculus of Variations : LP Spaces :  LP Spaces - Irene Fonseca

Modern Methods in the Calculus of Variations : LP Spaces

LP Spaces

Hardcover

Published: September 2007
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This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in Lp 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.

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 Lp-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 Lp-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 fur Mathematik, Vol. 156 (4), April, 2009)

Measure Theory and L[superscript p] Spaces
Measuresp. 3
L[superscript p] Spacesp. 139
The Direct Method and Lower Semicontinuity
The Direct Method and Lower Semicontinuityp. 231
Convex Analysisp. 247
Functionals Defined on L[superscript p]
Integrands f = f (z)p. 325
Integrands f = f (x, z)p. 379
Integrands f = f (x, u, z)p. 485
Young Measuresp. 517
Appendix
Functional Analysis and Set Theoryp. 549
Notes and Open Problemsp. 573
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387357843
ISBN-10: 038735784X
Series: Springer Monographs in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 600
Published: September 2007
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 3.18
Weight (kg): 1.09