Azagra Rueda, DanielFerrera Cuesta, JuanLópez-Mesas Colomina, FernandoRangel, Y.2023-06-202023-06-202007-02-150022-247X10.1016/j.jmaa.2006.03.088https://hdl.handle.net/20.500.14352/49817We 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.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022247X0600343Xrestricted access514.764.2Lipschitz functionRiemannian manifoldSmooth approximationHamilton-Jacobi equationsconvex functionsspacesGeometría diferencial1204.04 Geometría Diferencial