Existence of Solutions for Degenerate Elliptic Problems in Weighted Sobolev Space. (2nd December 2015) - Dai, Lili
Abstract : This paper is devoted to the study of the existence of solutions to a general elliptic problemA u + g ( x, u, ∇ u ) = f - div ⁡ F, withf ∈ L 1 ( Ω ) andF ∈ ∏ i = 1 N L p ' ( Ω, ω i * ), whereA is a Leray-Lions operator from a weighted Sobolev space into its dual andg ( x, s, ξ ) is a nonlinear term satisfyingg x, s, ξ sgn ⁡ ( s ) ≥ ρ ∑ i = 1 N ω i | ξ i | p, | s | ≥ h > 0, and a growth condition with respect toξ . Here, ω i, ω i * are weight functions that will be defined in the Preliminaries.