Degenerate elliptic problem with a singular nonlinearity. Issue 5 (4th May 2023)

• Record Type: Journal Article
• Authors: Sbai, Abdelaaziz; El hadfi, Youssef
• Is Part Of: Complex variables and elliptic equations. Volume 68:Issue 5(2023)
• Page Start: 701
• Page End: 718
• Publication Date: 2023-05-04
• Subjects: Degenerate elliptic equation -- singular nonlinearity -- existence -- regularity -- symmetrization -- Sobolev spaces; 35J60 -- 35J70 -- 35J75 -- 35B45 -- 35D30 -- 35B65; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2021.2014458
• Languages: English
• ISSNs: 1747-6933

Abstract

ABSTRACT: In this paper, we prove existence and regularity results for solutions of some nonlinear Dirichlet problems for an elliptic equation defined by a degenerate coercive operator and a singular right-hand side (1) { − div ( a ( x, u, ∇ u ) ) = f u γ in Ω, u = 0 on ∂ Ω, where Ω is bounded open subset of I R N ( N ≥ 2 ), γ > 0 and f is a non-negative function that belongs to some Lebesgue space.