Berrabeh, SouadRabah, Mecheter: Rapporteur2024-07-102024-07-102024https://dspace.univ-msila.dz/handle/123456789/43546in 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.enSobolev spacespseudo-monotoneoperator nonlinearelliptic equationweak solutionThesis