PARABOLIC HESSIAN EQUATIONS OUTSIDE A BOWL-SHAPED DOMAIN

被引：0

作者：

Dai, Limei ^{[1
]}

Guo, Xuewen ^{[2
]}

机构：

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

[2] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2024年 / 23卷 / 01期

关键词：

Parabolic Hessian equation; exterior problem; asymptotic behavior; bowl-shaped domain; EXTERIOR DIRICHLET PROBLEM; MONGE-AMPERE EQUATION; VISCOSITY SOLUTIONS; THEOREM; CALABI; EXISTENCE; JORGENS;

D O I：

10.3934/cpaa.2024002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we will study the parabolic Hessian equation -utSk(D2u) = g(x, t) outside a bowl-shaped domain, where g E C0(Rn+1) is a positive function, g(x, t) =1+ O(|x|2 -t)-beta /2, |x|2 -t-+ oo, n > 3, beta > 2 is a constant. Firstly, we construct the viscosity subsolutions and supersolutions of the parabolic Hessian equation. Then we use the Perron method to prove the existence and uniqueness of viscosity solutions with asymptotic behavior at infinity.

引用

页码：112 / 130

页数：19

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