Interior gradient bounds for local minimizers of variational integrals under nonstandard growth conditions

Inspired by the work of Marcellini and Papi, we consider local minima u: ℝ ⁿ ⊃ Ω → ℝ ^M of variational integrals ò_W h( | ?u | ) \int\limits_\Omega {h\left( {\left| {\nabla u} \right|} \right)} dx and prove interior gradient bounds under rather general assumptions on h provided that u is locally bounded. Our requirements on the density h do not involve the dimension n. Bibliography: 18 titles.