Abstract and Applied Analysis
Volume 2005 (2005), Issue 7, Pages 733-756
doi:10.1155/AAA.2005.733
Normal solvability of general linear
elliptic problems
1Department of Mathematics, Technion–Israel Institute of Technology, Haifa 32000, Israel
2Laboratoire deMathématiques Appliquées, UMR5585 CNRS, Université Lyon 1, Villeurbanne 69622, France
Received 13 June 2004
Copyright © 2005 A. Volpert and V. Volpert. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The paper is devoted to general elliptic problems in the
Douglis-Nirenberg sense. We obtain a necessary and sufficient
condition of normal solvability in the case of unbounded domains.
Along with the ellipticity condition, proper ellipticity and
Lopatinsky condition that determine normal solvability of
elliptic problems in bounded domains, one more condition
formulated in terms of limiting problems should be imposed in the
case of unbounded domains.