We obtain some W 2,2 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.
Abstract. This paper is concerning with the study of a class of weight functions and their properties. As an application, we prove some a priori bounds for a class of uniformly elliptic second order linear differential operators in weighted Sobolev spaces.Mathematics subject classification (2010): 35J25, 35B65, 35R05.
ABSTRACT. This paper deals with the Dirichlet problem for second order linear elliptic equations in unbounded domains of the plane in weighted Sobolev spaces. We prove an a priori bound and an existence and uniqueness result.
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