Weighted sobolev spaces and the nonlinear dirichlet problem in unbounded domains

1979 ◽  
Vol 121 (1) ◽  
pp. 319-336 ◽  
Author(s):  
V. Benci ◽  
D. Fortunato
Keyword(s):  
Dirichlet Problem ◽  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Nonlinear Dirichlet Problem

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.

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.

scholarly journals On Entropy Solutions of Anisotropic Elliptic Equations with Variable Nonlinearity Indices

2017 ◽  
Vol 63 (3) ◽  
pp. 475-493 ◽  
Author(s):  
L M Kozhevnikova
Keyword(s):  
Dirichlet Problem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Unbounded Domains ◽  
Second Order ◽  
Entropy Solutions ◽  
Anisotropic Sobolev Spaces ◽  
Right Hand ◽  
Anisotropic Elliptic Equations

For a certain class of second-order anisotropic elliptic equations with variable nonlinearity indices and L1 right-hand side we consider the Dirichlet problem in arbitrary unbounded domains. We prove the existence and uniqueness of entropy solutions in anisotropic Sobolev spaces with variable indices.

scholarly journals W2,p-Solvability of the Dirichlet Problem for Elliptic Equations with Singular Data

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Loredana Caso ◽  
Roberta D’Ambrosio ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Sobolev Spaces ◽  
Unique Solvability ◽  
Elliptic Equations ◽  
Weighted Sobolev Spaces ◽  
Elliptic Partial Differential Equations ◽  
Planar Case ◽  
Singular Data

We give an overview on some results concerning the unique solvability of the Dirichlet problem inW2,p,p>1, for second-order linear elliptic partial differential equations in nondivergence form and with singular data in weighted Sobolev spaces. We also extend such results to the planar case.

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.

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