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Let H be a Hilbert space, E?H be an arbitrary subset and f:E?R, G:E?H be two functions. We give a necessary and sufficient condition on the pair (f,G) for the existence of a convex function F?C1,1(H) such that F=f and ?F=G on E. We also show tha[...]texto impreso
We prove a general form of a fixed point theorem for mappings from a Riemannian manifold into itself which are obtained as perturbations of a given mapping by means of general operations which in particular include the cases of sum (when a Lie g[...]texto impreso
Azagra Rueda, Daniel ; Ferrera Cuesta, Juan ; López-Mesas Colomina, Fernando | Elsevier | 2003-07-01We establish approximate Rolle's theorems for the proximal subgradient and for the generalized gradient. We also show that an exact Rolle's theorem for the generalized gradient is completely false in all infinite-dimensional Banach spaces (even [...]texto impreso
We characterize the class of separable Banach spaces X such that for every continuous function f : X -> Rand for every continuous function epsilon : X -> (0, +infinity) there exists a C-1 smooth function g: X -> R for which vertical bar f(x) [...]texto impreso
Let X be a separable Banach space that admits a separating polynomial; in particular, let X be a separable Hilbert space. Let f : X -> R be bounded and Lipschitz, with uniformly continuous derivative. Then, for each epsilon > 0, there exists a[...]texto impreso
Azagra Rueda, Daniel ; Gómez Gil, Javier ; Fry, Robb ; Lovo, Mauricio ; Jaramillo Aguado, Jesús Ángel | Oxford University Press | 2005-03We show that if X is a Banach space having an unconditional basis and a Cp-smooth Lipschitz bump function, then for every C1-smooth function f from X into a Banach space Y, and for every continuous function ? : X ? (0, ?), there exists a Cp-smoo[...]texto impreso
In this article we examine the concentration and oscillation effects developed by high-frequency eigenfunctions of the Laplace operator in a compact Riemannian manifold. More precisely, we are interested in the structure of the possible invarian[...]texto impreso
We prove that for every infinite-dimensional Banach space X with a Frechet differentiable norm, the sphere S-X is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessaril[...]texto impreso
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The authors show that for every closed convex set C in a separable Banach space there is a nonnegative C1 convex function f such that C = {x: f(x) = 0}. The key is to show this for a closed halfspace. This result has several attractive consequen[...]texto impreso
Azagra Rueda, Daniel ; Fabián, M. ; Jiménez Sevilla, María del Mar | University of Toronto Press | 2005We establish sufficient conditions on the shape of a set A included in the space Ln s (X; Y ) of the n-linear symmetric mappings between Banach spaces X and Y , to ensure the existence of a Cn-smooth mapping f : X ¡! Y , with bounded support, an[...]texto impreso
In this paper we establish several results which allow to find fixed points and zeros of set-valued mappings on Riemannian manifolds. In order to prove these results we make use of subdifferential calculus. We also give some useful applications.texto impreso
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We consider the generalized evolution of compact level sets by functions of their normal vectors and second fundamental forms on a Riemannian manifold M. The level sets of a function u;M -> R evolve in such a way whenever u solves an equation u[...]texto impreso
Azagra Rueda, Daniel ; Jiménez Sevilla, María del Mar | Universidad de Extremadura, Departamento de Matemáticas | 2002While the topological and geometrical properties of convex bodies in Banach spaces are quite well understood (including their topological and smooth classification), much less is known about the structure of starlike bodies. Starlike bodies are [...]
