Extremal functions for a supercritical k-Hessian inequality of Sobolev-type. (August 2021)

• Record Type: Journal Article
• Authors: de Oliveira, José Francisco; Ubilla, Pedro
• Is Part Of: Nonlinear analysis. Volume 60(2021)
• Publication Date: 2021-08
• Subjects: 35J20 -- 35J60 -- 35J65 -- 35J50; k-Hessian -- Supercritical growth -- Extremal function -- Elliptic equations; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103314
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Our main purpose in this paper is to investigate a supercritical Sobolev-type inequality for the k -Hessian operator acting on Φ 0, rad k ( B ), the space of radially symmetric k -admissible functions on the unit ball B ⊂ R N . We also prove both the existence of admissible extremal functions for the associated variational problem and the solvability of a related k -Hessian equation with supercritical growth.