Azagra Rueda, Daniel and Ferrera Cuesta, Juan and Sanz Alonso, Beatriz (2008) Viscosity solutions to second order partial differential equations on Riemannian manifolds. Journal of Differential Equations, 245 (2). pp. 307-336. ISSN 0022-0396
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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, d(2)u) = 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 d2u in a uniformly continuous manner, then comparison results are established with no restrictive assumptions on curvature.
|Uncontrolled Keywords:||nonsmooth analysis; degenerate elliptic second order PDEs; Hamilton-Jacobi equations; viscosity solution; Riemannian manifold|
|Subjects:||Sciences > Mathematics > Differential equations|
|Deposited On:||17 Apr 2012 11:41|
|Last Modified:||06 Feb 2014 10:08|
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