RT Journal Article
T1 Viscosity solutions to second order partial differential equations on Riemannian manifolds
A1 Azagra Rueda, Daniel
A1 Ferrera Cuesta, Juan
A1 Sanz Alonso, Beatriz
AB 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.
PB Elsevier
SN 0022-0396
YR 2008
FD 2008-07-15
LK https://hdl.handle.net/20.500.14352/49815
UL https://hdl.handle.net/20.500.14352/49815
LA eng
NO MTM-
NO UCM-CAM
DS Docta Complutense
RD 18 abr 2025