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 in	Kragujevac Journal of Mathematics Vol. 44; no. 4; pp. 617 - 637
Main Authors	AHMEDATT, T., AHMED, A., HJIAJ, H., TOUZANI, A.
Format	Journal Article
Language	English
Published	01.01.2020
Online Access	Get full text
ISSN	1450-9628 2406-3045
DOI	10.46793/KgJMat2004.617A

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Summary:	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.
ISSN:	1450-9628 2406-3045
DOI:	10.46793/KgJMat2004.617A