On semilinear elliptic equations involving stummel classes - Abdelkrim, Maghni; Supervisor: Abdelaziz, Hellal; Co-Supervisor: Noureddine, Dechoucha (Mohamed Boudiaf University of M'sila, 2025)
This memory deals with the study of the existence, uniqueness, and regularity of semilinear elliptic equations, more precisely: ( −d i v(M(x)∇v)+ g (v) = f , v ∈ W 1,2 0 (Ω). Where Ω is a bounded open subset of R n (n Ê 3), In this case, we suppose that M(x) is nxn symmetric matrix, elliptic, bounded, and g : R → R is non decreasing, and Lipschitz. The datum f is taken belongs to S˜α(Ω), for α = 1or 2. Since the Stummel classes have some inclusion properties with other function spaces and appli cations to the regularity of the solution of elliptic partial differential equations, so our studying is based on employing Stampacchia’s lemma and a weighted embedding of a function in Stummel classes where the weight is in compactly supported Sobolev spaces.
Keywords: Stummel classes; Morrey spaces; Sobolev spaces; Hilbert spaces; Existence; Uniqueness; Regularity