We prove some existence, nonexistence and regularity results for the boundary value problem Δλu+f(u)=0in Ω,u| ∂Ω=0, where Ω is a bounded subset of RN, N<2, and Δλ is a Δλ- Laplacian, i.e. a "degenerate" elliptic operator of the kind Δλ:=∑i=1N ∂xi(λi2(x) ∂xi),λ=( λ1,..., λN). Together with some assumptions made in Franchi and Lanconelli (1984) [1], the family λ is supposed to verify a condition making Δλ homogeneous of degree two with respect to a group of dilations in RN.
On semilinear $Delta_lambda$-Laplace equation
KOGOJ, ALESSIA ELISABETTA;
2012
Abstract
We prove some existence, nonexistence and regularity results for the boundary value problem Δλu+f(u)=0in Ω,u| ∂Ω=0, where Ω is a bounded subset of RN, N<2, and Δλ is a Δλ- Laplacian, i.e. a "degenerate" elliptic operator of the kind Δλ:=∑i=1N ∂xi(λi2(x) ∂xi),λ=( λ1,..., λN). Together with some assumptions made in Franchi and Lanconelli (1984) [1], the family λ is supposed to verify a condition making Δλ homogeneous of degree two with respect to a group of dilations in RN.File in questo prodotto:
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