Hölder continuity of minimizers of functionals with non standard growth conditions (Q1199974)

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.