Abstract

We establish local higher integrability and differentiability results for minimizers of variational integrals F = ∫ΩF)dx over W1,p-Sobolev mappings v: Ω ⇢ Rn → RN satisfying a Dirichlet boundary condition. The integrands F are assumed to be autonomous, convex and of growth, but are otherwise not subjected to any further structure conditions, and we consider exponents in the range 1 < p ≤ q < p*, where p* denotes the Sobolev conjugate exponent of p