31 citations · 49 across the 10 of their papers we have counts for
12 papers
A counterexample to the pointwise validity of an asymptotic mean value property for -harmonic functions
Ángel Arroyo, Jeff Calder, Mikko Parviainen
We give a counterexample showing that an asymptotic mean value property for -harmonic functions in does not necessarily hold in the pointwise sense for a…
Existence of solutions for a system with general Hardy--Sobolev singular criticalities
Ángel Arroyo, Rafael López-Soriano, Alejandro Ortega
In this paper we study a class of Hardy--Sobolev type systems defined in and coupled by a singular critical Hardy--Sobolev term. The main novelty of this work is tha…
Local regularity estimates for general discrete dynamic programming equations
Ángel Arroyo, Pablo Blanc, Mikko Parviainen
We obtain an analytic proof for asymptotic Hölder estimate and Harnack's inequality for solutions to a discrete dynamic programming equation. The results also generalize to functio…
Hölder regularity for stochastic processes with bounded and measurable increments
Ángel Arroyo, Pablo Blanc, Mikko Parviainen
We obtain an asymptotic Hölder estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynami…
Inverse problems on low-dimensional manifolds
Giovanni S. Alberti, Ángel Arroyo, Matteo Santacesaria
We consider abstract inverse problems between infinite-dimensional Banach spaces. These inverse problems are typically nonlinear and ill-posed, making the inversion with limited an…
-harmonic functions by way of intrinsic mean value properties
Ángel Arroyo, José G. Llorente
Let be a bounded domain satisfying the uniform exterior cone condition. We establish existence and uniqueness of continuous solutions of the Dirichlet Proble…
Asymptotic Hölder Regularity for the Ellipsoid Process
Ángel Arroyo, Mikko Parviainen
We obtain an asymptotic Hölder estimate for functions satisfying a dynamic programming principle arising from a so-called ellipsoid process. By the ellipsoid process we mean a gene…
On a class of singular measures satisfying a strong annular decay condition
Ángel Arroyo, José G. Llorente
A metric measure space is said to satisfy the strong annular decay condition if there is a constant such that $$ μ\big(B(x,R)\setminus B(x,r)\big)\leq C\, \frac{R-r…
Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities
Ángel Arroyo, Hannes Luiro, Mikko Parviainen +1
We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in . The method of the proof is based on…
Tug-of-war games with varying probabilities and the normalized -Laplacian
Ángel Arroyo, Joonas Heino, Mikko Parviainen
We study a tug-of-war game with varying probabilities. In particular, we show that the value of the game is locally asymptotically Hölder continuous. We also show the existence and…
On the asymptotic mean value property for planar p-harmonic functions
Angel Arroyo, José G. Llorente
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…
On the Dirichlet problem for solutions of a restricted nonlinear mean value property
Ángel Arroyo, José G. Llorente
We give an analytic proof of the solution of Dirichlet Problem for continous functions satisfying a nonlinear mean value problem related to the p-laplace operator and certain stoch…