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Smooth approximation of Lipschitz functions on Riemannian manifolds



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Azagra Rueda, Daniel y Ferrera Cuesta, Juan y López-Mesas Colomina, Fernando y Rangel, Y. (2007) Smooth approximation of Lipschitz functions on Riemannian manifolds. Journal of Mathematical Analysis and Applications, 326 (2). pp. 1370-1378. ISSN 0022-247X

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URL Oficial: http://www.sciencedirect.com/science/article/pii/S0022247X0600343X


We show that for every Lipschitz function f defined on a separable Riemannian manifold M (possibly of infinite dimension), for every continuous epsilon : M -> (0, + infinity), and for every positive number r > 0, there exists a C-infinity smooth Lipschitz function g : M -> R such that vertical bar f(p) - g(p)vertical bar <= epsilon(p) for every p is an element of M and Lip(g) <= Lip(f) + r. Consequently, every separable Riemannian manifold is uniformly bumpable. We also present some applications of this result, such as a general version for separable Riemannian manifolds of Deville-Godefroy-Zizler's smooth variational principle.

Tipo de documento:Artículo
Palabras clave:Lipschitz function; Riemannian manifold; Smooth approximation; Hamilton-Jacobi equations; convex functions; spaces
Materias:Ciencias > Matemáticas > Geometría diferencial
Código ID:14761
Depositado:17 Abr 2012 11:44
Última Modificación:06 Feb 2014 10:08

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