Year: 2005
Type: article
Abstract: 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
Authors: Hicham G. Gebran, Charles A. Stuart
Institution: École Polytechnique Fédérale de Lausanne
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2024901087