Viscosity solutions to second order partial differential equations on Riemannian manifolds

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dc.creatorAzagra, Daniel
dc.creatorFerrera, Juan
dc.creatorSanz, Beatriz
dc.date2006-12-23
dc.date2008-03-13
dc.date.accessioned2026-07-07T09:26:28Z
dc.date.available2026-07-07T09:26:28Z
dc.descriptionWe 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 $d^{2}u$ in a uniformly continuous manner, then comparison results are established with no restrictive assumptions on curvature.
dc.descriptionFinal version: the domain of F in the equation F=0 has been changed in order to get more generality and simplicity in the definitions and assumptions, and several important misprints have been corrected
dc.identifierhttps://arxiv.org/abs/math/0612742
dc.identifierhttp://arxiv.org/abs/math/0612742
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156760
dc.subjectAnalysis of PDEs
dc.subjectDifferential Geometry
dc.subject58J32, 49J52, 49L25, 35D05, 35J70
dc.titleViscosity solutions to second order partial differential equations on Riemannian manifolds
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