𝑊𝟐,𝟐 A Priori Bounds for a Class of Elliptic Operators

Abstract

We obtain some 𝑊2,2 a priori bounds for a class of uniformly elliptic second-order differential operators, both in a no-weighted and in a weighted case. We deduce a uniqueness and existence theorem for the related Dirichlet problem in some weighted Sobolev spaces on unbounded domains.