Existence of Renormalized Solutions for Some Anisotropic Quasilinear Elliptic Equations

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DOI: 10.46793/KgJMat2004.617A


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=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.


Anisotropic Sobolev spaces, variable exponents, quasilinear elliptic equations, renormalized solutions.


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