scholarly journals An asymptotic-preserving method for highly anisotropic elliptic equations based on a Micro–Macro decomposition

2012 ◽  
Vol 231 (7) ◽  
pp. 2724-2740 ◽  
Author(s):  
Pierre Degond ◽  
Alexei Lozinski ◽  
Jacek Narski ◽  
Claudia Negulescu
Keyword(s):  
Elliptic Equations ◽  
Asymptotic Preserving ◽  
Anisotropic Elliptic Equations

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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