Critical growth problems with singular nonlinearities on Carnot groups. (October 2015)

• Record Type: Journal Article
• Authors: Loiudice, Annunziata
• Is Part Of: Nonlinear analysis. Volume 126(2015)
• Page Start: 415
• Page End: 436
• Publication Date: 2015-10
• Subjects: 35H20 -- 35J70; Subelliptic critical problem -- Singular nonlinearity -- Hardy–Sobolev extremal -- Carnot group; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.06.010
• Languages: English
• ISSNs: 0362-546X

Abstract

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.