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Raúl Fierro

Publications and source records attributed to Raúl Fierro.

6 recordsLinked to original sources
arXiv2026

Remarks on a Liouville-type theorem by Chae and Wolf for stationary Navier-Stokes equations

In this note, we revisit a Liouville-type theorem of Chae and Wolf for stationary Navier-Stokes equations in $\mathbb{R}^3$ [J. Differential Equations 261 (2016) 5541-5560]. We show that their logarithmic improvement of the classical $L^{9/2}$ condition is part of a substantially broader weighted framework. More precisely, we prove that a solution $u\in\dot H^1(\mathbb{R}^3)$ is necessarily trivial whenever $$ \int_{\mathbb{R}^3}|u(x)|^{9/2}\,ω(|u(x)|)\,dx< +\infty, $$ for every positive, nondecreasing and bounded weight $ω$ satisfying a mild growth condition near the origin. This structural condition encompasses the logarithmic weight due to Chae and Wolf, as well as a hierarchy of iterated-logarithmic weights and (genuinely) non-logarithmic examples, including a dyadic weight. Our result identifies a broader class of weighted integrability conditions under which the triviality of stationary Navier-Stokes solutions follows, and shows that the mechanism underlying the Chae-Wolf improvement is not intrinsically tied to a specific logarithmic weight or to a single logarithmic scale.

math.AP↗
arXiv2026

Sequential Stability of the Value Function and the Solution Mapping in Berge's Maximum Theorem via Variational Convergence

Berge's maximum theorem ensures the continuity of the value function and the upper semicontinuity of the solution mapping in parametric optimization problems. This theorem plays a central role in optimization theory, game theory, and dynamic programming. Motivated by the inherent inaccuracies in optimization data, this paper investigates the stability of such problems under sequential perturbations of both the objective function and the feasible mapping. The analysis focuses on the convergence of sequences of value functions and solution mappings via variational approximations of the data. To this end, we employ lower and upper continuous, epi- and hypo-convergence notions for functions, together with lower and upper continuous and graphical convergence notions for multifunctions. In addition, we study some relationships among these types of convergence and provide examples and counterexamples associated with the corresponding notions. Our results extend and complement existing stability results in the literature. We provide applications to generalized Nash equilibrium problems, where stability is obtained via a direct approach, as well as to finite-horizon dynamic programming models under novel perturbation assumptions.

math.OC↗
arXiv2022

Inverse maximum theorems and some consequences

We deal with inverse maximum theorems, which are inspired by the ones given by Aoyama, Komiya, Li et al., Park and Komiya, and Yamauchi. As a consequence of our results, we state and prove an inverse maximum Nash theorem and show that any generalized Nash game can be reduced to a classical Nash game, under suitable assumptions. Additionally, we show that a result by Arrow and Debreu, on the existence of solutions for generalized Nash games, is actually equivalent to the one given by Debreu-Fan-Glicksberg for classical Nash games, which in turn is equivalent to Kakutani-Fan-Glisckberg's fixed point theorem.

math.OC↗
arXiv2016

A model for risk assessment of a large earthquake with application to Chilean data

We study the asymptotic distribution for the occurrence time of the next large earthquake, by knowing the last large seismic event occurred a long time ago. We prove that, under reasonable conditions, such a distribution is asymptotically exponential with a rate depending on the asymptotic slope of the cumulative intensity function corresponding to a non-homogeneous Poisson process. Moreover, as it is not possible to obtain an empirical cumulative distribution function for the waiting time of the next large earthquake, a random cumulative function based on existing data is stated. We demonstrate that analogous results to the theorems of Glivenko-Cantelli and Kolmogorov are satisfied by this random cumulative function. We conduct a simulation study for detecting in what scenario the approximate distribution of the studied elapsed time performs well. Finally, a real-world data analysis is carried out to illustrate the potential applications of our proposal.

math.ST↗
arXiv2015

Condensing and Semi-continuous Multi-functions on Uniform Spaces

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in nonlinear analysis. An application of our results is given for operators defined on locally convex spaces. The main aim of this work is to unify some well-known results existing in complete metric and vector topological spaces.

math.GN↗