Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222711 | Nonlinear Analysis: Theory, Methods & Applications | 2018 | 16 Pages |
Abstract
In this paper we study the k-convex solutions to the boundary blow-up k-Hessian problem Sk(D2u)=H(x)up for xâΩ,u(x)â+â as dist(x,âΩ)â0.Here kâ{1,2,â¦,N},Sk(D2u) is the k-Hessian operator, and Ω is a smooth, bounded, strictly convex domain in RN(Nâ¥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.
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Authors
Xuemei Zhang, Meiqiang Feng,