Extending the well-known connection between classical linear potential theory and
probability theory (through the interplay between harmonic functions and martingales) to the …

This work is concerned with the gradient flow of absolutely p-homogeneous convex
functionals on a Hilbert space, which we show to exhibit finite (p< 2 p< 2) or infinite …

In this paper we study the evolution problem associated with the first fractional eigenvalue.
We prove that the Dirichlet problem with homogeneous boundary condition is well posed for …

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 dynamic …

We consider the elliptic differential operator defined as the sum of the minimum and the
maximum eigenvalue of the Hessian matrix, which can be viewed as a degenerate elliptic …

We consider the Dirichlet problem for partial trace operators which include the smallest and
the largest eigenvalue of the Hessian matrix. It is related to two-player zero-sum differential …

We investigate conditions for the existence and uniqueness of viscosity solutions of the
Dirichlet problem for a degenerate elliptic equation describing a stationary diffusion, which …

In this paper, we will study various Liouville-type theorems for partial trace equations with
nonlinear gradient terms. Specifically, we will provide sufficient conditions for non-negative …

In this paper, we study value functions of time-dependent tug-of-war games. We first prove
the existence and uniqueness of value functions and verify that these game values satisfy a …

In this paper we find viscosity solutions to a coupled system composed by two equations, the
first one is parabolic and driven by the infinity Laplacian while the second one is elliptic and …