Smooth approximation of Lipschitz functions on Riemannian manifolds

Journal of Mathematical Analysis and Applications

Volumn 326, Issue 2, 2007, Pages 1370-1378

  Azagra, D ^a   Ferrera, J ^a   Lopez Mesas F ^a   Rangel, Y ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Lipschitz function; Riemannian manifold; Smooth approximation

Indexed keywords

EID: 33750608260     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.03.088     Document Type: Article

References (13)

1. D. Azagra, J. Ferrera, Inf-convolution and regularization of convex functions on Riemannian manifolds of nonpositive curvature, Rev. Mat. Complut., in press
2. Azagra D., Ferrera J., and López-Mesas F. Nonsmooth analysis and Hamilton-Jacobi equations on Riemannian manifolds. J. Funct. Anal. 220 2 (2005) 304-361
3. 1-fine approximation of functions on Banach spaces with unconditional basis. Quart. J. Math. 56 1 (2005) 13-20
4. Deville R., Godefroy G., and Zizler V. A smooth variational principle with applications to Hamilton-Jacobi equations in infinite dimensions. J. Funct. Anal. 111 1 (1993) 197-212
5. Deville R., Godefroy G., and Zizler V. Smoothness and Renormings in Banach Spaces. Pitman Monographs Surveys Pure Appl. Math. vol. 64 (1993)
6. M.I. Garrido, J.A. Jaramillo, Y. Rangel, Algebras of differentiable functions on infinite-dimensional Riemannian manifolds, preprint
7. Greene R.E., and Wu H. On the subharmonicity and plurisubharmonicity of geodesically convex functions. Indiana Univ. Math. J. 22 (1972/1973) 641-653
8. ∞ convex functions and manifolds of positive curvature. Acta Math. 137 3-4 (1976) 209-245
9. ∞ approximations of convex, subharmonic, and plurisubharmonic functions. Ann. Sci. École Norm. Sup. (4) 12 1 (1979) 47-84
10. Lasry J.-M., and Lions P.-L. A remark on regularization in Hilbert spaces. Israel J. Math. 55 3 (1986) 257-266
11. Moulis N. Approximation de fonctions différentiables sur certains espaces de Banach. Ann. Inst. Fourier (Grenoble) 21 4 (1971) 293-345
12. Myers S.B. Algebras of differentiable functions. Proc. Amer. Math. Soc. 5 (1954) 917-922
13. Nakai M. Algebras of some differentiable functions on Riemannian manifolds. Japan. J. Math. 29 (1959) 60-67