Existence and regularity of the solution of some elliptic problems - Souad, Berrabeh; Rapporteur: Rabah, Mecheter (Mohamed Boudiaf University of M'sila, 2025)
in 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.
Keywords: Sobolev spaces; pseudo-monotone; operator nonlinear; elliptic equation; weak solution