We prove anLp-a priori bound,p>2, for solutions of second order linear elliptic partial differential equations in divergence form with discontinuous coefficients in unbounded domains.
We give an overview on some recent results concerning the study of the Dirichlet problem for second-order linear elliptic partial differential equations in divergence form and with discontinuous coefficients, in unbounded domains. The main theorem consists in an -a priori bound, . Some applications of this bound in the framework of non-variational problems, in a weighted and a non-weighted case, are also given.
Elliptic Equations with Discontinuous Coefficients in Weighted Sobolev Spaces on Unbounded Domains