Browsing by Author "Assia, boudjellal"

Now showing 1 - 1 of 1
  • 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.