Uniqueness of Solutions to Anisotropic Elliptic Equations with Nonpower Nonlinearities in Unbounded Domains

2016 ◽  
Vol 219 (1) ◽  
pp. 160-171
Author(s):  
L. M. Kozhevnikova ◽  
A. A. Khadzhi
Keyword(s):  
Elliptic Equations ◽  
Unbounded Domains ◽  
Uniqueness Of 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 and renormalized solutions for some nonlinear anisotropic elliptic equations with variable exponents and L 1-data

2021 ◽  
Vol 7 (2) ◽  
pp. 277-298
Author(s):  
Mostafa El Moumni ◽  
Deval Sidi Mohamed
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Variable Exponents ◽  
Renormalized Solutions ◽  
Nonlinear Elliptic ◽  
Anisotropic Elliptic Equations

Abstract We prove in this paper some existence and unicity results of entropy and renormalized solutions for some nonlinear elliptic equations with general anisotropic diffusivities and variable exponents. The data are assumed to be merely integrable.

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