Talenti, Giorgio Boundedness of minimizers. (English) Zbl 0723.58015 Hokkaido Math. J. 19, No. 2, 259-279 (1990). 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. Reviewer: Th.M.Rassias (Athens) Cited in 42 Documents MSC: 58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals 49Q15 Geometric measure and integration theory, integral and normal currents in optimization Keywords:minimizer; Euler equation; Sobolev space; Young functions; distribution; calculus of variations × Cite Format Result Cite Review PDF Full Text: DOI