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Spaces of Morrey type and elliptic equations in divergence form on unbounded domains. (English) Zbl 0881.35031
Summary: We study some function spaces of Morrey type. As an application of our results we consider the Dirichlet problem for a linear elliptic differential equation of second order in divergence form in an open, unbounded domain of \(\mathbb{R}^n\). We prove an a priori bound and an existence and uniqueness theorem.

35J25 Boundary value problems for second-order elliptic equations
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35B45 A priori estimates in context of PDEs