Boundary Value Problems
Volume 2009 (2009), Article ID 637243, 9 pages
doi:10.1155/2009/637243
Research Article

A Complement to the Fredholm Theory of Elliptic Systems on Bounded Domains

Patrick J. Rabier

Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

Received 24 March 2009; Revised 4 June 2009; Accepted 11 June 2009

Academic Editor: Peter Bates

Copyright © 2009 Patrick J. Rabier. 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

We fill a gap in the Lp theory of elliptic systems on bounded domains, by proving the p-independence of the index and null-space under “minimal” smoothness assumptions. This result has been known for long if additional regularity is assumed and in various other special cases, possibly for a limited range of values of p. Here, p-independence is proved in full generality.