Spaces of Morrey type and elliptic equations in divergence form on unbounded domains. (English) Zbl 0881.35031

Transirico, M.; Troisi, M.; Vitolo, A.

Boll. Unione Mat. Ital., VII. Ser., B 9, No. 1, 153-174 (1995).

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.

MSC:

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

Keywords:

Morrey space; existence; uniqueness