Existence of Renormalized Solutions for Some Anisotropic Quasilinear Elliptic Equations - AHMEDATT, T.; AHMED, A.; HJIAJ, H.; TOUZANI, A. (Kragujevac Journal of Mathematics, 2020)
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.