Regularity results for an anisotropic nonlinear Dirichlet problem
Fessel Achhoud, Giuseppa Rita Cirmi · Complex Variables and Elliptic Equations · 2024
In this paper we consider the homogeneous Dirichlet problem associated to the model equation −div(a(x)|∇u|p−2∇u)−div(|u|(r−1)q+1|∇u|q−2∇u)=finΩ, where Ω is a bounded open subset of RN,N>2, 1 1q′ and f belongs to Lm(Ω),m>1. We give some regularity results according to the values of the exponents (r−1)q+1 and m in suitable ranges depending on N,p and q.