Browsing by Author "Naasira, Bentoum"

Now showing 1 - 1 of 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.