Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity and with natural growth
In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second order discontinuous elliptic systems with nonlinearity and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global Hölder continuous in the case of the dimension without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets are always empty for...