5 papers
The Monge--Ampère equation on graphs
Ahmed Alkhozaae, Julio D. Rossi, Aelson Sobral +1
We introduce a version of the Monge--Ampère equation on finite graphs, motivated by nonlinear graph-based interpolation and semi-supervised learning. The operator is defined as the…
The evolution equation and the eigenvalue problem for the Laplacian in a regular tree
Leandro M. Del Pezzo, Nicolas Frevenza, Julio D. Rossi
In this paper, our main goal is to study the evolution problem associated with the Laplacian operator with Dirichlet boundary conditions on a regular tree. To this end, we place sp…
Game theoretical asymptotic mean value properties for non-homogeneous -Laplace problems
Félix del Teso, Julio D. Rossi
We extend the classical mean value property for the Laplacian operator to address a nonlinear and non-homogeneous problem related to the -Laplacian operator for . Specifica…
The limit as of the fractional convex envelope
Begoña Barrios, Leandro M. Del Pezzo, Alexander Quaas +1
We study the behavior of the fractional convexity when the fractional parameter goes to 1. For any notion of convexity, the convex envelope of a datum prescribed on the boundary of…
The evolution problem associated with the fractional first eigenvalue
Begoña Barrios, Leandro M. Del Pezzo, Alexander Quaas +1
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…