Critical growth problems with singular nonlinearities on Carnot groups. (October 2015) - Loiudice, Annunziata
Abstract: We provide regularity, existence and non existence results for the semilinear subelliptic problem with critical growth − Δ G u = ψ α | u | 2 ∗ ( α ) − 2 u d ( ξ ) α + λ u in Ω, u = 0 on ∂ Ω, where Δ G is a sublaplacian on a Carnot group G, 0 < α < 2, 2 ∗ ( α ) = 2 ( Q − α ) / ( Q − 2 ), Ω is a bounded domain of G, d is the natural gauge associated with the fundamental solution of − Δ G on G and ψ : = | ∇ G d |, ∇ G being the subelliptic gradient associated to Δ G, λ is a real parameter.