Everywhere regularity for a class of vectorial functionals under subquadratic general growth conditions

Abstract

AbstractWe consider the integral functional of the calculus of variations ∫Ωf(Du)dx, where f:RnN→R satisfies f(z)=g(|z|) and g is an N-function with subquadratic p–q growth. We prove that minimizers u:Ω⊂Rn→RN of such a functional are locally Lipschitz continuous, provided g verifies some additional conditions