相关论文: An obstacle problem for Tug-of-War games
Pursuing a new approach to the study of infinite games in combinatorics, we introduce the categories $\mathbf{Game}_{A}$ and $\mathbf{Game}_{B}$ and improve some classical results concerning topological games related to the duality between…
Subgame perfect equilibria are specific Nash equilibria in perfect information games in extensive form. They are important because they relate to the rationality of the players. They always exist in infinite games with continuous…
We prove a uniform boundary Harnack inequality for nonnegative harmonic functions of the fractional Laplacian on arbitrary open set $D$. This yields a unique representation of such functions as integrals against measures on $D^c\cup…
Generalizing the result of Li and Tam for the hyperbolic spaces, we prove an existence theorem on the Dirichlet problem for harmonic maps with $C^1$ boundary conditions at infinity between asymptotically hyperbolic manifolds.
We extend holomorphically polyharmonic functions on a real ball to a complex set being the union of rotated balls. We solve a Dirichlet type problem for complex polyharmonic functions with the boundary condition given on the union of…
We prove a higher regularity result for the free boundary in the obstacle problem for the fractional Laplacian via a higher order boundary Harnack inequality.
In this paper we are concerned with a two-penalty boundary obstacle problem of interest in thermics, fluid dynamics and electricity. Specifically, we prove existence, uniqueness and optimal regularity of the solutions, and we establish…
In the last decades, control problems with infinite horizons and discount factors have become increasingly central not only for economics but also for applications in artificial intelligence and machine learning. The strong links between…
Under a mild Lipschitz condition we prove a theorem on the existence and uniqueness of global solutions to delay fractional differential equations. Then, we establish a result on the exponential boundedness for these solutions.
This work advances knowledge of the threshold of prox-boundedness of a function; an important concern in the use of proximal point optimization algorithms and in determining the existence of the Moreau envelope of the function. In finite…
In Stackelberg v/s Stackelberg games a collection of leaders compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the followers. The resulting equilibrium problems are plagued by the nonuniqueness of…
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…
We consider the mixed problem for $L$ the Lam\'e system of elasticity in a bounded Lipschitz domain $ \Omega\subset\reals ^2$. We suppose that the boundary is written as the union of two disjoint sets, $\partial\Omega =D\cup N$. We take…
We study harmonic functions for the Laplace-Beltrami operator on the real hyperbolic ball. We obtain necessary and sufficient conditions for this functions and their normal derivatives to have a boundary distribution.In doing so, we put…
In the setting of a metric space equipped with a doubling measure supporting a $(1,1)$-Poincar\'e inequality, we study the problem of minimizing the BV-energy in a bounded domain $\Omega$ of functions bounded between two obstacle functions…
In this article we investigate the higher regularity properties of the regular free boundary in the fractional thin obstacle problem. Relying on a Hodograph-Legendre transform, we show that for smooth or analytic obstacles the regular free…
In this paper, we study a tug-of-war type operator on geometric graphs and its associated Dirichlet problem on a random data cloud. Specifically, we analyze the convergence of the value functions as the number of data points increases and…
Two boundary value problems for the Helmholtz equation in a semi-infinite strip are considered. The main feature of these problems is that, in addition to the function and its normal derivative on the boundary, the functionals of the…
This paper develops an algorithm for upper- and lower-bounding the value function for a class of linear time-varying games subject to convex control sets. In particular, a two-player zero-sum differential game is considered where the…
We use ideas from quantitative homogenization to show that nonconstant harmonic functions on the percolation cluster cannot satisfy certain structural constraints, for example, a Lipschitz bound. These unique-continuation-type results are…