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 \mathcal 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.