Hölder regularity of the solutions of some classes of elliptic systems in convex nonsmooth domains

Abstract

We prove, at first, the Hölder continuity up to the boundary of a convex nonsmooth domain of the weak solution of a linear second-order elliptic system in divergence form with discontinuous coefficients under a suitable condition on the dispersion of the eigenvalues of the coefficients matrix. We apply the above result to some classes of quasilinear and nonlinear elliptic systems. Moreover, we show existence and uniqueness of a very weak solution of a linear second-order elliptic system with discontinuous coefficients and L 1 -right-hand side extending an analogous result for one single equation due to Stampacchia.