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.
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页码：279 / 290
页数：12
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