Regularity for a class of variational integrals motivated by non-linear elasticity

Abstract

We amsider (local) minimizers u∈H^1,p(Ω,R^N) of variational integrals ℱ(u):=∫_Ωf(Du)dx with integrand f coming asymptotically close to |Du|^p for large values of Du and prove everywhere regularity theorems without imposing any differentiability or convexity conditions on f. Further sections contain applications to certain relaxed problems.