Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities

We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in $\Omega\subset \mathbb R^n$. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in $\Omega\times \Omega$ via couplings.Comment: 26 page

On the Dirichlet problem for solutions of a restricted nonlinear mean value property

Let Ω⊂Rd be a bounded domain and suppose that for each x∈Ω a radius r=r(x) is given so that the ball Bx=B(x,r) is contained in Ω. For 0≤α<1, we consider the following operator in C(¯¯¯¯Ω) Tαu(x)=α2(supBxu+infBxu)+(1−α)∫Bxu, and show that, under certain assumptions on Ω and the radius function r(x), the Dirichlet problem with continuous boundary data has a unique solution u∈C(¯¯¯¯Ω) satisfying Tαu=u. The motivation comes from the study of so called p-harmonious functions and certain stochastic games.Partially supported by grants MTM2011-24606, MTM2014-51824-P and 2014 SGR 75

A priori Hölder and Lipschitz regularity for generalized p-harmonious functions in metric measure spaces

Let (X, d, μ) be a proper metric measure space and let Ω ⊂ X be a bounded domain. For each x ∈ Ω, we choose a radius 0 < ϱ(x) ≤ dist(x, ∂Ω) and let Bx be the closed ball centered at x with radius ϱ(x). If α ∈ R, consider the following operator in C(Ω), Tαu(x) = α 2 (sup Bx u + inf Bx u) + 1 – α μ(Bx) ∫ Bx u dμ. Under appropriate assumptions on α, X, μ and the radius function ϱ we show that solutions u ∈ C(Ω) of the functional equation Tαu = u satisfy a local Hölder or Lipschitz condition in Ω. The motivation comes from the so called p-harmonious functions in euclidean domains.The research was partially supported by grants MTM2011-24606, MTM2014-51824-p and 2014 SGR 75

pp-harmonic functions by way of intrinsic mean value properties

Let $\Omega\subset\mathbb{R}^n$ be a bounded domain satisfying the uniform exterior cone condition. We establish existence and uniqueness of continuous solutions of the Dirichlet Problem associated to certain intrinsic nonlinear mean value properties in $\Omega$. Furthermore we show that, when properly normalized, such functions converge to the $p$-harmonic solution of the Dirichlet problem in $\Omega$, for $p\in[2,\infty)$. The proof of existence is constructive and the methods are entirely analytic, a fundamental tool being the construction of explicit, $p$-independent barrier functions in $\Omega$.Comment: 22 page

On the asymptotic mean value property for planar p-harmonic functions

We show that p-harmonic functions in the plane satisfy a nonlinear asymptotic mean value property for p > 1. This extends previous results of Manfredi and Lindqvist for certain range of p’s.Partially supported by grants MTM2011-24606, MTM2014-51824-P and 2014 SGR 75

Tug-of-war games with varying probabilities and the normalized p(x)-laplacian

We study a two player zero-sum tug-of-war game with varying probabilities that depend on the game location x. In particular, we show that the value of the game is locally asymptotically Hölder continuous. The main difficulty is the loss of translation invariance. We also show the existence and uniqueness of values of the game. As an application, we prove that the value function of the game converges to a viscosity solution of the normalized p(x) -Laplacian.Part of this research was done during a visit of Á. A. to the University of Jyväskylä in 2015. Á. A. was partially supported by grants MTM2011-24606, MTM2014-51824-P and 2014 SGR 75. M. P. was supported by the Academy of Finland project #260791

Effect of mold temperature on the impact behavior and morphology of injection molded foams based on polypropylene polyethylene–octene copolymer blends

Producción CientíficaIn this work, an isotactic polypropylene (PP) and a polyethylene–octene copolymer (POE) have been blended and injection-molded, obtaining solids and foamed samples with a relative density of 0.76. Different mold temperature and injection temperature were used. The Izod impact strength was measured. For solids, higher mold temperature increased the impact resistance, whereas in foams, the opposite trend was observed. In order to understand the reasons of this behavior, the morphology of the elastomeric phase, the crystalline morphology and the cellular structure have been studied. The presence of the elastomer near the skin in the case of high mold temperature can explain the improvement produced with a high mold temperature in solids. For foams, aspects as the elastomer coarsening in the core of the sample or the presence of a thicker solid skin are the critical parameters that justify the improved behavior of the materials produced with a lower mold temperature.Ministerio de Economía, Industria y Competitividad (grant DI-15-07952

Low density polyethylene/silica nanocomposite foams. Relationship between chemical composition, particle dispersion, cellular structure and physical properties

Postprint (author's final draft

Inverse problems on low-dimensional manifolds

We consider abstract inverse problems between infinite-dimensional Banach spaces. These inverse problems are typically nonlinear and ill-posed, making the inversion with limited and noisy measurements a delicate process. In this work, we assume that the unknown belongs to a finite-dimensional manifold: this assumption arises in many real-world scenarios where natural objects have a low intrinsic dimension and belong to a certain submanifold of a much larger ambient space. We prove uniqueness and H\"older and Lipschitz stability and derive a globally-convergent reconstruction algorithm from a finite number of measurements. Several examples are discussed.Comment: 35 pages, 5 figure