The Dirichlet Problem for elliptic equations in unbounded domains of the plane

In this paper we prove a uniqueness and existence theorem for the Dirichlet problem inW2,pfor second order linear elliptic equations in unbounded domains of the plane. Here the leading coefficients are locally of classVMOand satisfy a suitable condition at infinity.

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On Entropy Solutions of Anisotropic Elliptic Equations with Variable Nonlinearity Indices

Contemporary Mathematics. Fundamental Directions ◽

10.22363/2413-3639-2017-63-3-475-493 ◽

2017 ◽

Vol 63 (3) ◽

pp. 475-493 ◽

Cited By ~ 1

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.

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Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2008/582435 ◽

2008 ◽

Vol 2008 ◽

pp. 1-12 ◽

Cited By ~ 3

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.

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

Mathematica Slovaca ◽

10.2478/s12175-013-0173-7 ◽

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.

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A Priori Bounds for a Class of Elliptic Operators

International Journal of Differential Equations ◽

10.1155/2011/572824 ◽

2011 ◽

Vol 2011 ◽

pp. 1-17 ◽

Cited By ~ 3

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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