Hölder continuity of minimizers of functionals with non standard growth conditions. (English) Zbl 0773.49019

Moscariello, Gioconda; Nania, Luciana

Ric. Mat. 40, No. 2, 259-273 (1991).

The authors deal with the problem: under what conditions on the integrand \(f\) can one get the result that the local minima of the functional \(I(u)=\int_ \Omega f(| Du|)dx\) (considered on some classes of Sobolev spaces, \(\Omega\) being a bounded open set in \(\mathbb{R}^ n\), \(n\geq 1)\) are Hölder continuous or are locally bounded?
Several theorems giving a positive answer to the question above are proved under the assumptions that \(f\) is a nonnegative, convex, increasing function and satisfies some growth condition.

Reviewer: Z.Denkowski (Kraków)

MSC:

49N60

Regularity of solutions in optimal control

Keywords:

variational functions; local solutions; local boundedness of solutions