Regularity of minimizers of autonomous convex variational integrals

Abstract

We establish local higher integrability and differentiability results for minimizers of variational integrals $$\mathfrak{F}(v,\Omega )={\int }_{\Omega }/!F(Dv(x))dx$$ over $W^{1,p}$--Sobolev mappings $u:\Omega \subset {\mathbb{R}}^n\to {\mathbb{R}}^N$ 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 $1<p\le q<p^{\ast }$, where $p^{\ast }$ denotes the Sobolev conjugate exponent of $p$.

Cited by in corpus (3)

• Regularity results for a class of obstacle problems with $p,q-$growth conditions
• Lipschitz bounds for nonuniformly elliptic integral functionals in the plane
• Existence and regularity results for weak solutions to $(p,q)$-elliptic systems in divergence form