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.

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

2008 ◽  
Vol 6 (1) ◽  
pp. 47-58 ◽  
Author(s):  
Paola Cavaliere ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Existence Theorem ◽  
Elliptic Equations ◽  
Unbounded Domains ◽  
Suitable Condition ◽  
Second Order ◽  
Order Linear ◽  
Uniqueness And Existence

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.

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.

scholarly journals Entropy Solutions for Nonlinear Elliptic Anisotropic Homogeneous Neumann Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
B. K. Bonzi ◽  
S. Ouaro ◽  
F. D. Y. Zongo
Keyword(s):  
Weak Solution ◽  
Neumann Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Entropy Solution ◽  
Boundary Value ◽  
Entropy Solutions ◽  
Approximation Methods ◽  
Nonlinear Elliptic ◽  
Anisotropic Elliptic Equations

We prove the existence and uniqueness of entropy solution for nonlinear anisotropic elliptic equations with Neumann homogeneous boundary value condition for -data. We prove first, by using minimization techniques, the existence and uniqueness of weak solution when the data is bounded, and by approximation methods, we prove a result of existence and uniqueness of entropy solution.

Orlicz and Sobolev spaces on unbounded domains

1975 ◽  
Vol 342 (1630) ◽  
pp. 373-400 ◽  
Keyword(s):  
Dirichlet Problem ◽  
Unbounded Domain ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Orlicz Function ◽  
Unbounded Domains ◽  
Compact Embedding ◽  
Embedding Theorems ◽  
Natural Embedding ◽  
Compact Map

This paper deals with embedding theorems involving the Sobolev spaces H m,p (Ω) and H 0 m , p ( Ω ) on an unbounded domain Ω in R n ( n > 1 ) . It is shown, for example, that the Sobolev space H 0 1 , n ( Ω ) is continuously embedded in the Orlicz space L Φ* (Ω), where Φ ( t ) = | t | n exp ⁡ ( | t | n / ( n − 1 ) ) ; and that multiplication by suitable functions acts as a compact map of H 0 1 , n ( Ω ) to L Ψ ∗ ( Ω ) for any Orlicz function Ψ subordinate to Φ in a certain sense. These results extend the earlier work of Trudinger, who dealt with the case in which Ω is bounded. Examples are given of unbounded domains Ω for which the natural embedding of in H 1 , p ( Ω ) in L p ( Ω ) ( 1 < p < ∞ ) is a k -set contraction for some k < 1: the case k = 0 corresponds to a compact embedding. Applications are made to the Dirichlet problem in an unbounded domain for elliptic equations with violent non-linearities.

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