On Entropy Solutions of Anisotropic Elliptic Equations with Variable Nonlinearity Indices in Unbounded Domains

2021 ◽  
Author(s):  
L. M. Kozhevnikova
Keyword(s):  
Elliptic Equations ◽  
Unbounded Domains ◽  
Entropy Solutions ◽  
Anisotropic Elliptic Equations

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 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.

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