The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations

被引：0

作者：

Dai, Limei ^{[1
]}

机构：

[1] Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Shandong, Peoples R China

来源：

ANALYSIS IN THEORY AND APPLICATIONS | 2022年

基金：

中国国家自然科学基金;

关键词：

Hessian equations; exterior Dirichlet problem; asymptotic behavior; MONGE-AMPERE EQUATION; THEOREM; EXTENSION; EXISTENCE; JORGENS; CALABI;

D O I：

10.4208/ata.OA-2022-0009xx2022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the exterior Dirichlet problem of Hessian equations sigma k(lambda(D2u)) = g(x) with g being a perturbation of a general positive function at infinity. The existence of the viscosity solutions with generalized asymptotic behavior at infinity is established by the Perron's method which extends the previous results for Hessian equations. By the solutions of Bernoulli ordinary differential equations, the viscosity subsolutions and supersolutions are constructed.

引用

页数：27

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