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FREDHOLM AND PROPERNESS PROPERTIES OF QUASILINEAR ELLIPTIC SYSTEMS OF SECOND ORDER

Published online by Cambridge University Press:  15 February 2005

Hicham G. Gebran  and
Charles A. Stuart
Hicham G. Gebran
Affiliation:
IACS-FSB, Ecole Polytechnique Fédérale Lausanne, CH-1015 Lausanne, Switzerland (hicham.gebran@epfl.ch; charles.stuart@epfl.ch)
Charles A. Stuart
Affiliation:
IACS-FSB, Ecole Polytechnique Fédérale Lausanne, CH-1015 Lausanne, Switzerland (hicham.gebran@epfl.ch; charles.stuart@epfl.ch)
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Abstract

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For a large class of subsets $\varOmega\subset\mathbb{R}^{N}$ (including unbounded domains), we discuss the Fredholm and properness properties of second-order quasilinear elliptic operators viewed as mappings from $W^{2,p}(\varOmega;\mathbb{R}^{m})$ to $L^{p}(\varOmega;\mathbb{R}^{m})$ with $N\ltp\lt\infty$ and $m\geq1$. These operators arise in the study of elliptic systems of $m$ equations on $\varOmega$. A study in the case of a single equation ($m=1$) on $\mathbb{R}^{N}$ was carried out by Rabier and Stuart.

AMS 2000 Mathematics subject classification: Primary 35J45; 35J60. Secondary 47A53; 47F05

Keywords

Fredholm operatorpropernessquasilinear elliptic operator
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 48 , Issue 1 , February 2005 , pp. 91 - 124
Copyright
Copyright © Edinburgh Mathematical Society 2005