Abstract and Applied Analysis
Volume 2005 (2005), Issue 7, Pages 733-756

Normal solvability of general linear elliptic problems

A. Volpert1 and V. Volpert2

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.


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.