Biblioteca de la Universidad Complutense de Madrid

Viscosity solutions to second order partial differential equations on Riemannian manifolds

Impacto

Azagra Rueda, Daniel y Ferrera Cuesta, Juan y 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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URL Oficial: http://www.sciencedirect.com/science/article/pii/S0022039608001630



Resumen

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.


Tipo de documento:Artículo
Palabras clave:nonsmooth analysis; degenerate elliptic second order PDEs; Hamilton-Jacobi equations; viscosity solution; Riemannian manifold
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:14758
Depositado:17 Abr 2012 11:41
Última Modificación:06 Feb 2014 10:08

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