Boundary blow-up solutions to the k-Hessian equation with singular weights

被引：30

作者：

Zhang, Xuemei ^{[1
]}

Feng, Meiqiang ^{[2
]}

机构：

[1] North China Elect Power Univ, Dept Math & Phys, Beijing 102206, Peoples R China

[2] Beijing Informat Sci & Technol Univ, Sch Appl Sci, Beijing 100192, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2018年 / 167卷

基金：

中国国家自然科学基金; 北京市自然科学基金;

关键词：

k-Hessian equation; Boundary blow up; Sub-supersolution method; k-convex solution; 2ND-ORDER ELLIPTIC-EQUATIONS; MONGE-AMPERE EQUATION; DIRICHLET PROBLEM; BEHAVIOR; EXISTENCE;

D O I：

10.1016/j.na.2017.11.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 is an element of Omega, u(x) -> +infinity as dist(x, partial derivative Omega) -> 0. Here k is an element of {1, 2,..., N}, S-k(D(2)u) is the k-Hessian operator, and Omega is a smooth, bounded, strictly convex domain in RN (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. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：51 / 66

页数：16

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