A priori bounds in \(L^p\) and in \(W^{2, p}\) for solutions of elliptic equations (Q2318938)

Summary: 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.