Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-03T00:39:44.421Z Has data issue: false hasContentIssue false

FREDHOLM AND PROPERNESS PROPERTIES OF QUASILINEAR ELLIPTIC SYSTEMS OF SECOND ORDER

Published online by Cambridge University Press:  15 February 2005

Hicham G. Gebran
Affiliation:
IACS-FSB, Ecole Polytechnique Fédérale Lausanne, CH-1015 Lausanne, Switzerland ([email protected]; [email protected])
Charles A. Stuart
Affiliation:
IACS-FSB, Ecole Polytechnique Fédérale Lausanne, CH-1015 Lausanne, Switzerland ([email protected]; [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2005