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 $|\xi|^p,$ $p \geq 2.$