Regularity of minimizers of some variational integrals with discontinuity

Abstract

We prove regularity properties in the vector valued case for minimizers of variational integrals of the form $$A(u)={\int }_{\Omega }A(x,u,Du)dx$$ where the integrand $A(x,u,Du)$ is not necessarily continuous respect to the variable $x,$ grows polinomially like $|\xi {|}^p,$ $p\ge 2.$