Abstract and Applied Analysis
Volume 2003 (2003), Issue 3, Pages 129-181

Properness and topological degree for general elliptic operators

V. Volpert1 and A. Volpert2

1Mathématiques Appliquées, UMR 5585 CNRS, Université Lyon 1, Villeurbanne 69622, France
2Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel

Received 29 November 2001

Copyright © 2003 V. Volpert and A. 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 operators in Hölder spaces in bounded or unbounded domains. We discuss the Fredholm property of linear operators and properness of nonlinear operators. We construct a topological degree for Fredholm and proper operators of index zero.