Nonlinear degenerate elliptic equations in weighted Sobolev spaces
Texas State University, Department of Mathematics
We study the existence of solutions for the nonlinear degenerated elliptic problem -div α(x, u, ∇u) = ƒ in Ω u = 0 on ∂Ω, where Ω is a bounded open set in ℝN, N ≥ 2, α is a Carathéodory function having degenerate coercivity α(x, u, ∇u)∇u ≥ v(x)b(|u|)|∇u|p, 1 < p < N, v(∙) is the weight function, b is continuous and ƒ ∈ Lr(Ω).
Nonlinear degenerated elliptic operators, Weighted Sobolev space, Monotony and rearrangement methods
Benali, A., & Jaouad, B. (2020). Nonlinear degenerate elliptic equations in weighted Sobolev spaces. <i>Electronic Journal of Differential Equations, 2020</i>(105), pp. 1-15.