scholarly journals Exponential decay and Fredholm properties in second-order quasilinear elliptic systems

2010 ◽  
Vol 249 (1) ◽  
pp. 94-117 ◽  
Author(s):  
Hicham G. Gebran ◽  
Charles A. Stuart
Keyword(s):  
Exponential Decay ◽  
Elliptic Systems ◽  
Second Order ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

scholarly journals FREDHOLM AND PROPERNESS PROPERTIES OF QUASILINEAR ELLIPTIC SYSTEMS OF SECOND ORDER

2005 ◽  
Vol 48 (1) ◽  
pp. 91-124 ◽  
Author(s):  
Hicham G. Gebran ◽  
Charles A. Stuart
Keyword(s):  
Large Class ◽  
Unbounded Domains ◽  
Elliptic Systems ◽  
Single Equation ◽  
Elliptic Operators ◽  
Second Order ◽  
Subject Classification ◽  
Secondary 47A53 ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

AbstractFor 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

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