This article is cited in 2 papers

Solvability of Boundary Value Problems for Quasielliptic Systems in Weighted Sobolev Spaces

L. N. Bondar

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: In the paper we consider boundary value problems for a class of quasielliptic systems in a half-space. The boundary value problems be assumed to satisfy the Lopatinskii condition. We establish unique solvability of the boundary value problems in weighted Sobolev spaces. We obtain sufficient solvability conditions for the boundary value problems and give an example when these solvability conditions are necessary.

Keywords: quasielliptic system, boundary value problem, Lopatinskii condition, weighted Sobolev space, solvability condition.

UDC: 519.635.4

Received: 27.03.2009

 English version: Journal of Mathematical Sciences, 2012, 186:3, 364–378