Complutense University Library

Viscosity solutions to second order partial differential equations on Riemannian manifolds

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

[img] PDF
Restricted to Repository staff only until 31 December 2020.

287kB

Official URL: http://www.sciencedirect.com/science/article/pii/S0022039608001630

View download statistics for this eprint

==>>> Export to other formats

Abstract

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.

Item Type:Article
Uncontrolled Keywords:nonsmooth analysis; degenerate elliptic second order PDEs; Hamilton-Jacobi equations; viscosity solution; Riemannian manifold
Subjects:Sciences > Mathematics > Differential equations
ID Code:14758
Deposited On:17 Apr 2012 11:41
Last Modified:06 Feb 2014 10:08

Repository Staff Only: item control page