Nouibat, WassilaSupervisor: Mecheter, Rabah2023-07-032023-07-032023-06-10http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/39908In this work, we study the existence and regularity of a weak and entropy solutions of elliptic problem (P) defined by (P) I Au u == 0f on on ∂Ω; Ω, the operator Au = −div(| ∇u |p−2 ∇u), 1 < p < ∞ is a pseudo-monotone operator, f ∈ M(Ω) or f ∈ L1(Ω). The method of solving our problem consist of obtaining local estimates for suitable approximate problems and then passing to the limit.enSobolev spaces, pseudo-monotone, operator nonlinear, elliptic equation, weak solution, entropy solution.Thesis