Oxford District, Reino Unido
We establish local higher integrability and differentiability results for minimizers of variational integrals F(v,) = Z F(Dv(x)) dx overW1,p-Sobolev mappings v : ⇢ Rn !RN satisfying a Dirichlet boundary condition. The integrands F are assumed to be autonomous, convex and of (p, q) 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.
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