Azagra Rueda, Daniel and Ferrera Cuesta, Juan and López-Mesas Colomina, Fernando and 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
![[img]](/style/images/fileicons/application_pdf.png) | PDF Restricted to Repository staff only until 31 December 2020. 135Kb |
Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X0600343X
Abstract
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Lipschitz function; Riemannian manifold; Smooth approximation; Hamilton-Jacobi equations; convex functions; spaces |
| Subjects: | Sciences > Mathematics > Differential geometry |
| ID Code: | 14761 |
| Deposited On: | 17 Apr 2012 13:44 |
| Last Modified: | 17 Apr 2012 13:44 |
Repository Staff Only: item control page
