A critical problem on the Hardy–Sobolev inequality in boundary singularity case. (September 2017)

• Record Type: Journal Article
• Authors: Hashizume, Masato
• Is Part Of: Nonlinear analysis. Volume 160(2017)
• Page Start: 70
• Page End: 78
• Publication Date: 2017-09
• Subjects: boundary singularity -- Hardy–Sobolev inequality -- minimization problem -- Neumann problem; 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.2017.05.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study a Neumann problem with the Hardy–Sobolev nonlinearity. In boundary singularity case, the impact of the mean curvature at singularity on existence of least-energy solution is well known. Existence and nonexistence of least-energy solution is studied by Hashizume (2017) except for lower dimension case. In this paper, we improve this previous work. More precisely, we study four dimensional case and show existence of minimizer in critical case in some sense.