zbMATH — the first resource for mathematics

Boundedness of minimizers. (English) Zbl 0723.58015
The author finds conditions guaranteeing that solutions to typical problems of the calculus of variations are bounded. More precisely the following variational problem is studied: \[ \int_{G}f(u,Du)dx=\min imum,\quad u=g\text{ on } \partial G, \] where G, f, g are given; G is an open subset of Euclidean space \({\mathbb{R}}^ n\); n denotes the dimension that is greater than one; competing functions u are assumed to have scalar values; D stands for the gradient and \(dx=dx_ 1...dx_ n\), the Lebesgue n-dimensional measure. It is a nice paper with interesting proofs of the results obtained.

58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
Full Text: DOI