Browsing by Author "Rabah, Mecheter: Rapporteur"

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    Existence and regularity of the solution of some elliptic problems
    (Mohamed Boudiaf University of M'sila, 2024) Berrabeh, Souad; Rabah, Mecheter: Rapporteur
    in this work, we prove the existence and regularity of a weak solutions of elliptic problem (P) defined by (P) ( Au = f in Ω; u = 0 on ∂Ω, the operator Au = −div(| ∇u | p−2 ∇u), 1 < p < ∞ is a pseudo-monotone operator, f ∈ L 1 (Ω). The method of solving our problem consist of obtaining local estimates for suitable approximate problems and then passing to the limit.
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    Nonlinear weighted elliptic problem with degenerate coercivity and L 1 data
    (Mohamed Boudiaf University of M'sila, 2024-06) Mohammed, Bouguerra; Rabah, Mecheter: Rapporteur
    In this work, we prove the existence of a weak solution of elliptic problem (P) defined by: (P) ( −div(a(x) |∇u| p−2∇u 1+|u| ) + e(x)|u| p−2u = f in Ω; u = 0 on ∂Ω, with f ∈ L 1 (Ω) and the operator Au = −div(a(x) |∇u| p−2∇u 1+|u| ), 1 < p < ∞ is not coercive on W 1,p 0 (Ω) despite being well-defined between W 1,p 0 (Ω) and its dual W−1,p0 (Ω). Degenerate coercivity implies that as |u| becomes large, 1 1+|u| tends to zero. To solve this issue, we are going to approximate the operator by employing truncations in 1 1+|u| to obtain a coercive differential operator. Next, we will prove some a priori estimates on the sequence of approximate solutions, and we shall finally pass to the limit in the approximate problems to establish the existence of a weak solution for the problem (P).