Título: | Regularization by sup-inf convolutions on Riemannian manifolds: An extension of Lasry-Lions theorem to manifolds of bounded curvature |
Autores: | Azagra Rueda, Daniel ; Ferrera Cuesta, Juan |
Tipo de documento: | texto impreso |
Editorial: | Academic Press, 2015-03-15 |
Dimensiones: | application/pdf |
Nota general: | info:eu-repo/semantics/openAccess |
Idiomas: | |
Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Geometría diferencial , Tipo = Artículo |
Resumen: |
We show how Lasry-Lions's result on regularization of functions defined on R-n or on Hilbert spaces by sup inf convolutions with squares of distances can be extended to (finite or infinite dimensional) Riemannian manifolds M of bounded sectional curvature. More specifically, among other things we show that if the sectional curvature K of M satisfies -K-0 = 0, and if the injectivity and convexity radii of M are strictly positive, then every bounded, uniformly continuous function f : M -> R can be uniformly approximated by globally C-1,C-1 functions defined by (f(lambda))(mu) = sup(z is an element of M nu is an element of M)inf {f(y) + 1/2 lambda d(z, y)(2) - 1/2 mu d(x, z)(2)} as lambda, mu -> 0(+), with 0 |
En línea: | https://eprints.ucm.es/33309/1/Azagra33.pdf |
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