Información del autor
Autor Azagra Rueda, Daniel |
Documentos disponibles escritos por este autor (46)
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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 [...]texto impreso
Let U subset of R-d be open and convex. We prove that every (not necessarily Lipschitz or strongly) convex function f:U -> R can be approximated by real analytic convex functions, uniformly on all of U. We also show that C-0-fine approximation[...]texto impreso
We show that if X is a Banach space whose dual X* has an equivalent locally uniformly rotund (LUR) norm, then for every open convex U subset of X, for every real number epsilon > 0, and for every continuous and convex function f : U -> R (not [...]texto impreso
Heterochrony, evolutionary modifications in the rates and/or the timing of development, is widely recognized as an important agent of evolutionary change. In this paper, we are concerned with the detection of this evolutionary mechanism through [...]texto impreso
We show how an operation of inf-convolution can be used to approximate convex functions with $C^1$ smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some other pr[...]texto impreso
Starlike bodies are interesting in nonlinear functional analysis because they are strongly related to bump function sand to n-homogeneous polynomials on Banach spaces, and their geometrical proper ties are thus worth studying. In this paper we d[...]texto impreso
Azagra Rueda, Daniel ; Ferrera Cuesta, Juan ; López-Mesas Colomina, Fernando | Elsevier | 2006-11-01We establish a maximum principle for viscosity subsolutions and supersolutions of equations of the form u(t) + F(t, d(x)u) = 0, u(0, x) = u(0)(x), where u(0): M -> R is a bounded uniformly continuous function, M is a Riemannian manifold, and F:[...]texto impreso
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Azagra Rueda, Daniel ; Ferrera Cuesta, Juan ; López-Mesas Colomina, Fernando | Elsevier | 2005-03-15We establish some perturbed minimization principles, and we develop a theory of subdifferential calculus, for functions defined on Riemannian manifolds. Then we apply these results to show existence and uniqueness of viscosity solutions to Hamil[...]texto impreso
We prove that every function f:Rn?R satisfies that the image of the set of critical points at which the function f has Taylor expansions of order n?1 and non-empty subdifferentials of order n is a Lebesgue-null set. As a by-product of our proof,[...]texto impreso
The paper deals with the question, what can be said about smooth negligibility of compacta in those Banach spaces with smooth partitions of unity? It is inspired by the following theorem of Victor Klee and related results: If X is a non-reflexiv[...]texto impreso
Azagra Rueda, Daniel ; Jiménez Sevilla, María del Mar ; Deville, Robert | Cambridge University Press | 2003-01We study the size of the range of the derivatives of a smooth function between Banach spaces. We establish conditions on a pair of Banach spaces X and Y to ensure the existence of a C-p smooth (Frechet smooth or a continuous G (a) over cap teaux[...]texto impreso
We study the size of the sets of gradients of bump functions on the Hilbert space l(2), and the related question as to how small the set of tangent hyperplanes to a smooth bounded starlike body in l(2) can be. We find that those sets can be quit[...]texto impreso
Starlike bodies are interesting in nonlinear analysis because they are strongly related to polynomials and smooth bump functions, and their topological and geometrical properties are therefore worth studying. In this note we consider the questio[...]texto impreso
Azagra Rueda, Daniel ; Fry, Robb ; Montesinos Matilla, Luis Alejandro | America Mathematical Society | 2004-10-21We show that if Y is a separable subspace of a Banach space X such that both X and the quotient X/Y have C-p-smooth Lipschitz bump functions, and U is a bounded open subset of X, then, for every uniformly continuous function f : Y boolean AND U [...]texto impreso
We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold M. We give some applications of this theory, concerning, for instance, a Borwein-Preiss type variational principle on a Rie[...]texto impreso
Let X be a separable Banach space with a separating polynomial. We show that there exists C > = 1 (depending only on X) such that for every Lipschitz function f : X -> R, and every epsilon > 0, there exists a Lipschitz, real analytic function [...]texto impreso
We prove that every infinite-dimensional Banach space X having a (not necessarily equivalent) real-analytic norm is real-analytic diffeomorphic to X \ {0}. More generally, if X is an infinite-dimensional Banach space and F is a closed subspace o[...]texto impreso
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[...]texto impreso
Azagra Rueda, Daniel ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. ; Sánchez de los Reyes, Víctor Manuel | Academic Press | 2009-06If f is continuous on the interval [a, b], g is Riemann integrable (resp. Lebesgue measurable) on the interval [alpha, beta] and g([alpha, beta]) subset of [a, b], then f o g is Riemann integrable (resp. measurable) on [alpha, beta]. A well-know[...]texto impreso
In this note we prove that if a differentiable function oscillates between y« and « on the boundary of the unit ball then there exists a point in the interior of the ball in which the differential of the function has norm equal or less than« . T[...]texto impreso
We establish a second order smooth variational principle valid for functions defined on (possibly infinite- dimensional) Riemannian manifolds which are uniformly locally convex and have a strictly positive injectivity radius and bounded sectiona[...]texto impreso
Azagra Rueda, Daniel ; Ferrera Cuesta, Juan ; López-Mesas Colomina, Fernando ; Rangel, Y. | Elsevier | 2007-02-15We 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 smoo[...]texto impreso
Let X be a Banach space with a separable dual X*. Let Y subset of X be a closed subspace, and f : Y -> R a C(1)-smooth function. Then we show there is a C(1) extension of f to X.texto impreso
Let X be an infinite-dimensional Banach space, and let A be a CP Lipschitz bounded starlike body (for instance the unit ball of a smooth norm). We prove that.texto impreso
This article deals with smooth removability of compact sets in infinite-dimensional Banach spaces. The main result states that ifX is an infinite-dimensional Banach space which has a not necessarily equivalent Cp-smooth norm and K is a compact s[...]texto impreso
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Two main results presented by the authors include a mean-value inequality for a class of Gateaux subdifferentiable functions and a subdifferential Rolle’s theorem in a Banach space. For the second part, if a (Gateaux/Fréchet)subdifferentiable fu[...]texto impreso
We prove the following new characterization of Cp Lipschitz) smoothness in Banach spaces. An infinite-dimensional Banach space X has a Cp smooth (Lipschitz) bump function if and only if it has another Cp smooth (Lipschitz) bump function f such t[...]texto impreso
We prove that every continuous mapping from a separable infinite-dimensional Hilbert space X into R-m can be uniformly approximated by C-infinity-smooth mappings with no critical points. This kind of result can be regarded as a sort of strong ap[...]texto impreso
We prove comparison, uniqueness and existence results for viscosity solutions to a wide class of fully nonlinear second order partial differential equations F(x, u, du, d(2)u) = 0 defined on a finite-dimensional Riemannian manifold M. Finest res[...]texto impreso
Let C be a subset of ?n (not necessarily convex), f : C ? R be a function and G : C ? ?n be a uniformly continuous function, with modulus of continuity ?. We provide a necessary and sufficient condition on f, G for the existence of a convex func[...]