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Tug-of-War games and parabolic problems with spatial and time dependence
(Khayyam Publishing, 2014)
In this paper we use probabilistic arguments (Tug-of-War games) to obtain existence of viscosity solutions to a parabolic problem of the form {K(x,t)(Du)ut(x,t)=12⟨D2uJ(x,t)(Du),J(x,t)(Du)(x,t)⟩u(x,t)=F(x)in ΩT,on Γ, where ...
A limiting free boundary problem with gradient constraint and Tug-of-War games
(Springer Heidelberg, 2019-01)
In this manuscript we deal with regularity issues and the asymptotic behaviour (as p → ∞) of solutions for elliptic free boundary problems of p−Laplacian type (2 ≤ p < ∞): −pu(x) + λ0(x)χ{u>0}(x) = 0 in ⊂ RN , with a ...
Tug-of-War games and the infinity Laplacian with spatial dependence
(Amer Inst Mathematical Sciences, 2013-05)
In this paper we look for PDEs that arise as limits of values
of Tug-of-War games when the possible movements of the game are
taken in a family of sets that are not necessarily euclidean balls. In this
way we ¯nd existence ...
The unique continuation property for a nonlinear equation on trees
(Wiley, 2014-01)
In this paper, we study the game p-Laplacian on a tree, that is, u(x) = α / 2 max y∈S(x) u(y) + min y∈S(x) u(y) + β m y∈S(x) u(y);here x is a vertex of the tree and S(x) is the set of successors of x. We study the family ...
Global climate and energy policy after the COVID-19 pandemic : the tug-of-war between markets and politics
Before the COVID-19 pandemic of 2020, international climate diplomacy had
settled into a regular yet disturbing routine. Every year, governments gathered to negotiate their climate commitments. Progress was haphazard and ...
Maximal operators for the P-laplacian family
(Pacific Journal Mathematics, 2017-04)
We prove existence and uniqueness of viscosity solutions for the problem: max-Δp1u(x), -Δp2u(x) = f(x) in a bounded smooth domain Ω⊂ℝN with u=g on ∂Ω. Here -Δpu=(N+ p)-1|Du|2-pdiv (|Du|p-2Du) is the 1-homogeneous p-Laplacian ...
Juegos de tipo Tug-of-War y soluciones viscosasTug-of-War games and viscosity solutions
(2018-10-30)
La motivación de esta tesis es el estudio de los juegos llamados Tug-of-War en la literatura, y su conexión con ecuaciones en derivadas parciales (EDP). Consideramos diferentes variantes de juegos de dos jugadores, con ...
Obstacle problem and maximal operators
(De Gruyter, 2016-01)
Fix two differential operators L1 and L2, and define a sequence of functions inductively by considering u1 as the solution to the Dirichlet problem for an operator L1 and then un as the solution to the obstacle problem for ...
Transport Properties of Melanosomes along Microtubules Interpreted by a Tug-of-War Model with Loose Mechanical Coupling
(Public Library of Science, 2012-08)
In this work, we explored theoretically the transport of organelles driven along microtubules by molecular motors of opposed polarities using a stochastic model that considers a Langevin dynamics for the cargo, independent ...