Souad, BerrabehRapporteur: Rabah, Mecheter2025-07-152025-07-152025-06-15https://repository.univ-msila.dz/handle/123456789/47200in 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<p< is a pseudo-monotone operator, SEL¹(2). 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