Boundary blow-up solutions to the k-Hessian equation with singular weights. (January 2018)

• Record Type: Journal Article
• Authors: Zhang, Xuemei; Feng, Meiqiang
• Is Part Of: Nonlinear analysis. Volume 167(2018)
• Page Start: 51
• Page End: 66
• Publication Date: 2018-01
• Subjects: 34B18 -- 34B15 -- 34A34; k-Hessian equation -- Boundary blow up -- Sub-supersolution method -- k-convex solution; 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.2017.11.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study the k -convex solutions to the boundary blow-up k -Hessian problem S k ( D 2 u ) = H ( x ) u p for x ∈ Ω, u ( x ) → + ∞ as dist ( x, ∂ Ω ) → 0 . Here k ∈ { 1, 2, …, N }, S k ( D 2 u ) is the k -Hessian operator, and Ω is a smooth, bounded, strictly convex domain in R N ( N ≥ 2 ) . We show the existence, nonexistence, uniqueness results, global estimates and estimates near the boundary for the solutions. Our approach is largely based on the construction of suitable sub- and super-solutions.