Regularity of minimizers of some variational integrals with discontinuity

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

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