Viscosity Solutions to Second Order Parabolic PDEs on Riemannian Manifolds |
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Authors: | Xuehong Zhu |
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Institution: | (2) Department of Mathematics, Saitama University, Saitama, Japan; |
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Abstract: | 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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Keywords: | |
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