A Priori Bounds in L p and in W 2 , p for Solutions of Elliptic Equations

Abstract

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 $L^p$-a priori bound, $P>1$. Some applications of this bound in the framework of non-variational problems, in a weighted and a non-weighted case, are also given.