Browsing by Author "Rapporteur: Rabah, Mecheter"

Now showing 1 - 3 of 3
  • Thumbnail Image
    ItemOpen Access
    Degenerate elliptic equations with lower-order terms and L 1 data
    (Mohamed Boudiaf University of M'sila, 2025-06-15) Assia, boudjellal; Rapporteur: Rabah, Mecheter
    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.
  • Thumbnail Image
    ItemOpen Access
    Existence and regularity of the solution of some elliptic problems
    (Mohamed Boudiaf University of M'sila, 2025-06-15) Souad, Berrabeh; Rapporteur: Rabah, Mecheter
    in this work, we prove the existence and regularity of a weak solutions of elliptic problem (P) defined by (P) { Au fin 2: u= 0 on 20, the operator Audiv( Vu - Vu), 1
  • Thumbnail Image
    ItemOpen Access
    Weak Solutions for elliptic equations with lower-order terms and L 1 data
    (Mohamed Boudiaf University of M'sila, 2025-06-15) Naasira, Bentoum; Rapporteur: Rabah, Mecheter
    In this work, we study the existence of weak solutions for a class of linear elliptic equations with lower-order terms and integrable data. More precisely, we consider problems of the form:   − u = 0 div( , M(x)∇u) + a(x)u = f(x), in on Ω ∂ , Ω,  where Ω ⊂ R N is a bounded domain, M(x) is an elliptic matrix, a(x) ∈ L 1 (Ω), and f ∈ L 1 (Ω). Since the right-hand side lies in L 1 (Ω), standard variational methods are not applicable. To address this, we construct a sequence of approximate problems whose solutions are well-defined, and establish uniform a priori estimates. Then, using compactness arguments and the theory of pseudo-monotone operators, we prove the existence of a weak solution to the original problem.