Nonlinear weighted elliptic equations with L 1 data - Djerida, Chaima; Rabah, Mecheter: Supervisor (Mohamed Boudiaf University of M'sila, 2024)
in this work, we prove the existence of a weak solution of elliptic problem (P) defined by (P) ( −div(S(x)|∇u| p−2∇u) + e(x)|u| p−2u = f in Ω; u = 0 on ∂Ω, with f ∈ L 1 (Ω). The weighted p-Laplacian operator Au = −div(S(x)|∇u| p−2∇u), 1 < p < ∞ is a pseudo-monotone operator on W 1,p 0 (Ω) despite being well-defined between W 1,p 0 (Ω) and its dual W−1,p0 (Ω). The method of solving our problem consist of obtaining local estimates for suitable approximate problems and then passing to the limit.
Keywords: Weighted Sobolev spaces; pseudo-monotone; operator nonlinear; elliptic equation; weak solution