Existence and Regularity of Solutions to Degenerate Nonlinear p-Laplacian Elliptic Equations with a Low-Order Term
Year: 2025
Type: article
Abstract: In this paper we study the existence and regularity of solutions for a class of non linear degenerate elliptic equations−div a(x,∇u) (1+u)γ(p−1) + u = f(x), in Ω, u =0, on ∂Ω. Here 1 < p < 2 and γ ≥ 0, while f(x) ≥ 0 is a function in some Lebesuge space. Due to the presence of nonlinear terms, traditional variational methods are not applicable. Therefore, this paper begins by utilizing a truncation technique to derive an approximate equation, from which the existence and non-negativity of the approximate solution are obtained using Lions’ results and estimates. The approximate solution is then estimated using test functions, Hölder inequality, Fatou lemma, and other methods. This estimation ensures that the solution to the original problem can be obtained through the passage to the limit from the solution of the approximating problem. Finally, the existence of the solution to the original problem is proven using the control convergence theorem, Vitali’s theorem, and other related methods, leading to the uniqueness of the solution.
Source: Theoretical and Natural Science
Author: Jiayao Yan
Institution: University of Shanghai for Science and Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4412494973