Viscosity Solutions to Second Order Parabolic PDEs on Riemannian Manifolds

被引：5

作者：

Zhu, Xuehong ^{[1
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Sch Sci, Nanjing 210016, Peoples R China

来源：

ACTA APPLICANDAE MATHEMATICAE | 2011年 / 115卷 / 03期

关键词：

Parabolic PDEs; Riemannian manifold; Viscosity solution; PARTIAL-DIFFERENTIAL-EQUATIONS;

D O I：

10.1007/s10440-011-9621-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we consider viscosity solutions to second order parabolic PDEs u (t) +F(t,x,u,du,d (2) u)=0 defined on complete Riemannian manifolds with boundary conditions. We prove comparison, uniqueness and existence results for the solutions. Under the assumption that the manifold M has nonnegative sectional curvature, we get the finest results. If one additionally requires F to depend on d (2) u in a uniformly continuous manner, the assumptions on curvature can be thrown away.

引用

页码：279 / 290

页数：12

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