Viscosity Solutions to Second Order Partial Differential Equations on Riemannian Manifolds
نویسندگان
چکیده
We prove comparison, uniqueness and existence results for viscosity solutions to a wide class of fully nonlinear second order partial differential equations F (x, u, du, du) = 0 defined on a finite-dimensional Riemannian manifold M . Finest results (with hypothesis that require the function F to be degenerate elliptic, that is nonincreasing in the second order derivative variable, and uniformly continuous with respect to the variable x) are obtained under the assumption that M has nonnegative sectional curvature, while, if one additionally requires F to depend on du in a uniformly continuous manner, then comparison results are established with no restrictive assumptions on curvature.
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