Partial regularity of minimizers of functionals with discontinuous coefficients of low integrability with applications to nonlinear elliptic systems

Abstract

In this article, we consider minimizers of the functionalwhere is open and bounded and . We show that even though the coefficient a satisfies only that , it nonetheless follows that u is partially Hölder continuous on the set of regular points of Da. We note that the integrability exponent q > 1 is arbitrary, and so, the coefficient map can be very irregular. As an application we show that weak solutions of the elliptic systemsatisfies the same partial Hölder continuity. The model case we have in mind isFinally, we also demonstrate that Du is also almost everywhere Hölder continuous.