عنوان

Direct Methods in the Calculus of Variations

3642514405

9783642514401

b569583

Direct Methods in the Calculus of Variations

[Book]

by Bernard Dacorogna.

Berlin, Heidelberg

Springer Berlin Heidelberg

1989

(ix, 308 pages 10 illustrations)

Applied mathematical sciences (Springer-Verlag New York Inc.), 78.

Introduction --; Preliminaries --; General Setting and the Scalar Case --; The Vectorial Case --; Non-Convex Integrands --; Appendix: Applications --; Bibliography --; Index.

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.

Differential equations, Partial.

Mathematics.

Systems theory.

by Bernard Dacorogna.

Bernard Dacorogna

[Book]

Y