A priori bounds in Lp and in W2,p for solutions of elliptic equations

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 a Lp-a priori bound, p > 1. Some applications of this bound in the framework of non variational problems, in a weighted and a no-weigthed case, are also given

The Dirichlet problem for elliptic equations in unbounded domains of the plane

In this paper we prove a uniqueness and existence theorem for the Dirichlet problem in W^{2,p} for second order linear elliptic equations in unbounded domains of the plane. Here the leading coefficients are locally of class VMO and satisfy a suitable condition at infinity

A priori estimates for elliptic equations in weighted Sobolev spaces

In this paper we prove some a priori bounds for the solutions of the Dirichlet problem for elliptic equations with singular coefficients in weighted Sobolev spaces

The Dirichlet problem for elliptic equations in weighted Sobolev spaces

In this paper we prove some existence and uniqueness results for the Dirichlet problem for elliptic equations with singular coefficients in weighted Sobolev spaces

Uniqueness result for elliptic equations in unbounded domains

Following the strean of ideas of two recent papers of Chiarenza-Frasca-Longo, we establish a uniqueness result for the Dirichlet problem for a class of second order elliptic differential equations with discontinuous coefficients in unbounded domains of R^n, n>2

Second order elliptic equations with discontinuous coefficients in irregular domains

In the paper we study the Dirichlet problem for a class of linear second order elliptic equations in non divergence form in an open subset of R^n with irregular boundary. We suppose the coefficients discontinuous and singular on a subset of the boundary