Nonlinear degenerate elliptic equations in weighted Sobolev spaces
Date
2020-10-12
Authors
Benali, Aharrouch
Jaouad, Bennouna
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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).
Description
Keywords
Nonlinear degenerated elliptic operators, Weighted Sobolev space, Monotony and rearrangement methods
Citation
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.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.