Degenerate elliptic equations with lower-order terms and L 1 data
| dc.contributor.author | Assia, boudjellal | |
| dc.contributor.author | Rapporteur: Rabah, Mecheter | |
| dc.date.accessioned | 2025-07-03T09:40:19Z | |
| dc.date.available | 2025-07-03T09:40:19Z | |
| dc.date.issued | 2025-06-15 | |
| dc.description.abstract | This thesis investigates the existence of weak solutions for a class of degenerate elliptic equations with lower-order terms and right-hand side data in L 1 (Ω). The problem under consideration is of the form: −div M 1 + (x) | ∇ u| u ! + g(x)u = f(x) in Ω, u = 0 on ∂Ω, where Ω ⊂ R N is a bounded open domain, M(x) is a bounded and elliptic matrix, g(x) ∈ L 1 (Ω) is a nonnegative lower-order coefficient, and f(x) ∈ L 1 (Ω) satisfies a domination condition of the type |f(x)| ≤ kg(x). Due to the lack of coercivity and low regularity of the data, we introduce a sequence of approximate problems using truncation functions to regularize the nonlinear operator. We then establish uniform a priori estimates for the approximate solutions in H0 1 (Ω) ∩ L ∞(Ω). Finally, we pass to the limit in the nonlinear terms using compactness and weak convergence techniques to prove the existence of a bounded weak solution to the original problem. | |
| dc.identifier.uri | https://repository.univ-msila.dz/handle/123456789/46633 | |
| dc.language.iso | en | |
| dc.publisher | Mohamed Boudiaf University of M'sila | |
| dc.subject | degenerate elliptic equations | |
| dc.subject | lower-order terms | |
| dc.subject | pseudo-monotone operator | |
| dc.subject | L 1 -data | |
| dc.subject | bounded weak solution | |
| dc.title | Degenerate elliptic equations with lower-order terms and L 1 data | |
| dc.type | Thesis |