Entropy solution for a nonlinear degenerate elliptic problem with Dirichlet-type boundary condition and singular term

Abstract

This paper establishes the existence of entropy solutions for a class of nonlinear elliptic equations governed by a degenerate coercive operator and featuring a singular right-hand side, exemplified by the model case:

-div( (|∇u - Θ(u)|^p-2 (∇u - Θ(u)) ) / ( (1+|u|)^λ(p-1) ) ) + |u|^q-1u = f / u^γ   in Ω,
u ≥ 0   in Ω,
u = 0   on ∂Ω,

with Ω is a bounded open domain in R^N (N≥2), p>1, λ≥0, γ≥0, q≥1, f is a non-negative function that belongs to L¹(Ω) and Θ is assumed to be continuous on the real line R.