Introduction au calcul des variations / Bernard Dacorogna

The book has seven chapters: in the introduction various examples of problems of the calculus of variations are given, in chapter 1 the author introduces the function spaces used afterwards and some notions of convex analysis. In the second chapter he presents for the minimum of an integral functional the classical conditions of Euler-Lagrange, Hamilton- Jacobi, Weierstrass and Hilbert. In the following chapter the author exposes the direct method for the existence of a minimum in some Sobolev space for a convex and coercive integrand. The regularity results in particular for unidimensional integrals are exposed in chapter 4. In chapter 5 the author studies the problem of minimal surfaces, where he cannot use results of chapter 4: he examines in detail the bidimensional case, giving some generalities on surfaces and he exposes the Douglas theorem for the Plateau problem. The last chapter is reserved for isoperimetric inequalities in two or more dimensions. The work is a rigorous introduction to the calculus of variations for graduate students. (Zentralblatt)

Bibliogr. p. 205-207. Index