Direct Methods in the Calculus of Variations
By: by Bernard Dacorogna
Series: Applied Mathematical Sciences -- 78; Applied mathematical sciences (Springer-Verlag New York Inc.) -- 78.
Publisher: Springer Berlin Heidelberg
Published: 1989
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 308
ISBN-13: 9783642514425; 9783642514401
Subjects: Mathematics; Mathematical optimization; Partial Differential equations; Systems theory
Description: This book deals with the calculus of variations and presents the so called direct methods for proving existence of minima. It is divided into four main parts. The first one deals with the scalar case, i.e. with real-valued functions; it gives well known existence theorems and studies some of the classical necessary conditions such as Euler equations. The second part is concerned with vector-valued functions; some necessary or sufficient conditions are studied as well as several examples. The third one deals with the relaxation of nonconvex problems. Finally in the Appendix several examples of applications of the previous chapters to nonlinear elasticity and optimal design are given. The book serves an important purpose in bringing together, in the second and third parts as well as the Appendix, material which till now remained scattered in the literature. It thus gives a unified view of some of the recent developments. As special emphasis is laid on examples throughout, it will be useful also to readers interested in applications.
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Table of contents: title: Introduction; title: Preliminaries; title: General Setting and the Scalar Case; title: The Vectorial Case; title: Non-Convex Integrands; title: Appendix: Applications; title: Bibliography; title: Index.