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Inspired by the work of Marcellini and Papi, we consider local minima u: ℝ n  ⊃ Ω → ℝ M  of variational integrals $$ \int\limits_\Omega {h\left( {\left| {\nabla u} \right|} \right)} $$ 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.

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