RETRACTED ARTICLE: A $${C^{1,\alpha}}$$ partial regularity result for non-autonomous convex integrals with discontinuous coefficients

Abstract

We establish the \({C^{1,\alpha}}\) partial regularity of vectorial minimizers of non autonomous convex integral functionals of the type $$\mathcal{F}(u;\,\Omega):=\int_{\Omega}f(x, Du)\, dx,$$ with p-growth into the gradient variable. As a novel feature, we allow discontinuous dependence on the x variable, through a suitable Sobolev function. The Holder’s continuity of the gradient of the minimizers is obtained outside a negligible set and this an unavoidable feature in the vectorial setting. Here, the so called singular set has to take into account also of the possible discontinuity of the coefficients.