Boundary behavior of large solutions to a class of Hessian equations

Article type: Research Article

Authors: Mi, Ling^{a; *} | Chen, Chuan^b

Affiliations: [a] School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan, Shandong, 250353, China | [b] School of Cyber Security, Qilu University of Technology (Shandong Academy of Sciences), Jinan, Shandong, 250353, China

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In this paper, we consider the m-Hessian equation Sm[D2u]=b(x)f(u)>0 in Ω, subject to the singular boundary condition u=∞ on ∂Ω. We give estimates of the asymptotic behavior of such solutions near ∂Ω when the nonlinear term f satisfies a new structure condition.

Keywords: Hessian equations, singular boundary condition, asymptotic behavior

DOI: 10.3233/ASY-201656

Journal: Asymptotic Analysis, vol. 125, no. 1-2, pp. 187-202, 2021