Resumen de Regularity of minimizers of autonomous convex variational integrals

Menita Carozza, Jan Kristensen, Antonia Passarelli di Napoli

• 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.