Existence of Renormalized Solutions for Some Anisotropic Quasilinear Elliptic Equations

In this paper, we consider a class of anisotropic quasilinear elliptic equations of the type ( | ∑N { − ∂ia (x, u, ∇u ) + |u|s(x )− 1u = f (x,u ), in Ω, i |( i=1 u = 0 on ∂ Ω, where f(x,s) is a Carathéodory function which satisfies some growth condition. We prove the existence of renormalized solutio...

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Published inKragujevac Journal of Mathematics Vol. 44; no. 4; pp. 617 - 637
Main Authors AHMEDATT, T., AHMED, A., HJIAJ, H., TOUZANI, A.
Format Journal Article
LanguageEnglish
Published 01.01.2020
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ISSN1450-9628
2406-3045
DOI10.46793/KgJMat2004.617A

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Abstract In this paper, we consider a class of anisotropic quasilinear elliptic equations of the type ( | ∑N { − ∂ia (x, u, ∇u ) + |u|s(x )− 1u = f (x,u ), in Ω, i |( i=1 u = 0 on ∂ Ω, where f(x,s) is a Carathéodory function which satisfies some growth condition. We prove the existence of renormalized solutions for our Dirichlet problem, and some regularity results are concluded.
AbstractList In this paper, we consider a class of anisotropic quasilinear elliptic equations of the type ( | ∑N { − ∂ia (x, u, ∇u ) + |u|s(x )− 1u = f (x,u ), in Ω, i |( i=1 u = 0 on ∂ Ω, where f(x,s) is a Carathéodory function which satisfies some growth condition. We prove the existence of renormalized solutions for our Dirichlet problem, and some regularity results are concluded.
Author TOUZANI, A.
AHMED, A.
AHMEDATT, T.
HJIAJ, H.
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Cites_doi 10.1007/BFb0104029
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