Embedding and compactness theorems for irregular and unbounded domains in weighted Sobolev spaces

1986 ◽  
Vol 47 (1-2) ◽  
pp. 95-107
Author(s):  
S. Salerno ◽  
M. Troisi
Keyword(s):  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Compactness Theorems

scholarly journals Two-Scale Regularity for Homogenization Problems with Nonsmooth Fine Scale Geometry

2003 ◽  
Vol 13 (07) ◽  
pp. 1053-1080 ◽  
Author(s):  
A.-M. Matache ◽  
J. M. Melenk
Keyword(s):  
Detailed Analysis ◽  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Wave Number ◽  
Critical Parameters ◽  
Fine Scale ◽  
Cell Problem ◽  
Regularity Results ◽  
Homogenization Problems

Elliptic problems on unbounded domains with periodic coefficients and geometries are analyzed and two-scale regularity results for the solution are given. These are based on a detailed analysis in weighted Sobolev spaces of the so-called unit-cell problem in which the critical parameters (the period ε, the wave number t, and the differentiation order) enter explicitly.

scholarly journals Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Serena Boccia ◽  
Sara Monsurrò ◽  
Maria Transirico
Keyword(s):  
Uniqueness Theorem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
A Priori ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Regularity Result ◽  
Second Order ◽  
Order Linear ◽  
A Priori Bound

We study in this paper a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of , . We obtain an a priori bound, and a regularity result from which we deduce a uniqueness theorem.

The Dirichlet problem for elliptic equations in weighted Sobolev spaces on unbounded domains of the plane

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Serena Boccia ◽  
Maria Salvato ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
A Priori ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Uniqueness Result ◽  
Order Linear ◽  
A Priori Bound

AbstractThis paper deals with the Dirichlet problem for second order linear elliptic equations in unbounded domains of the plane in weighted Sobolev spaces. We prove an a priori bound and an existence and uniqueness result.

Equations of p-Laplacian Type in Unbounded Domains

2002 ◽  
Vol 2 (3) ◽  
Author(s):  
Pablo L. De Nápoli ◽  
M. Cristina Mariani
Keyword(s):  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Mountain Pass ◽  
Infinitely Many Solutions ◽  
Solutions To Equations

AbstractThis work is devoted to study the existence of solutions to equations of the p Laplacian type in unbounded domains. We prove the existence of at least one solution, and under further assumptions, the existence of infinitely many solutions. We apply the mountain pass theorem in weighted Sobolev spaces.

scholarly journals A Priori Bounds for a Class of Elliptic Operators

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Sara Monsurrò ◽  
Maria Salvato ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Existence Theorem ◽  
Sobolev Spaces ◽  
Differential Operators ◽  
A Priori ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Elliptic Operators ◽  
A Priori Bounds ◽  
Uniqueness And Existence

We obtain some a priori bounds for a class of uniformly elliptic second-order differential operators, both in a no-weighted and in a weighted case. We deduce a uniqueness and existence theorem for the related Dirichlet problem in some weighted Sobolev spaces on unbounded domains.

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