Asymptotic Formulas for Eigenvalues of Elliptic Operators of Second Order in unbounded Domains of the Maz'ja Class

1990 ◽  
Vol 145 (1) ◽  
pp. 281-295 ◽  
Author(s):  
Günter Berger
Keyword(s):  
Unbounded Domains ◽  
Elliptic Operators ◽  
Second Order ◽  
Asymptotic Formulas

The Dirichlet Problem for Second Order Elliptic Operators on Unbounded Domains

1985 ◽  
Vol 19 (2-3) ◽  
pp. 201-216 ◽  
Author(s):  
W. Walter ◽  
Rainer Janben ◽  
V. Besov
Keyword(s):  
Dirichlet Problem ◽  
Unbounded Domains ◽  
Elliptic Operators ◽  
Second Order ◽  
Second Order Elliptic Operators

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

scholarly journals Generalized principal eigenvalues of convex nonlinear elliptic operators in ℝN

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Anup Biswas ◽  
Prasun Roychowdhury
Keyword(s):  
Eigenvalue Problem ◽  
Principal Eigenvalue ◽  
Unbounded Domains ◽  
Elliptic Operators ◽  
Maximum Principles ◽  
Generalized Eigenvalues ◽  
Nonlinear Elliptic ◽  
Generalized Eigenvalue ◽  
General Convex ◽  
Appl Math

AbstractWe study the generalized eigenvalue problem in {\mathbb{R}^{N}} for a general convex nonlinear elliptic operator which is locally elliptic and positively 1-homogeneous. Generalizing [H. Berestycki and L. Rossi, Generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains, Comm. Pure Appl. Math. 68 2015, 6, 1014–1065], we consider three different notions of generalized eigenvalues and compare them. We also discuss the maximum principles and uniqueness of principal eigenfunctions.

scholarly journals Heat Kernels of Second Order Complex Elliptic Operators and Applications

1998 ◽  
Vol 152 (1) ◽  
pp. 22-73 ◽  
Author(s):  
Pascal Auscher ◽  
Alan McIntosh ◽  
Philippe Tchamitchian
Keyword(s):  
Elliptic Operators ◽  
Heat Kernels ◽  
Second Order ◽  
Order Complex

Some results on second-order elliptic operators with polynomially growing coefficients in L-spaces

2021 ◽  
pp. 125209
Author(s):  
Sallah Eddine Boutiah ◽  
Loredana Caso ◽  
Federica Gregorio ◽  
Cristian Tacelli
Keyword(s):  
Elliptic Operators ◽  
Second Order ◽  
Second Order Elliptic Operators

scholarly journals The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients

2014 ◽  
Vol 361 (3-4) ◽  
pp. 863-907 ◽  
Author(s):  
Steve Hofmann ◽  
Carlos Kenig ◽  
Svitlana Mayboroda ◽  
Jill Pipher
Keyword(s):  
Elliptic Operators ◽  
Second Order ◽  
Regularity Problem ◽  
Measurable Coefficients ◽  
Second Order Elliptic Operators ◽  
Complex Valued
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