Search results for "Nonlocal problems"
showing 3 items of 3 documents
A Monge-Kantorovich mass transport problem for a discrete distance
2011
This paper is concerned with a Monge-Kantorovich mass transport problem in which in the transport cost we replace the Euclidean distance with a discrete distance. We fix the length of a step and the distance that measures the cost of the transport depends of the number of steps that is needed to transport the involved mass from its origin to its destination. For this problem we construct special Kantorovich potentials, and optimal transport plans via a nonlocal version of the PDE formulation given by Evans and Gangbo for the classical case with the Euclidean distance. We also study how these problems, when rescaling the step distance, approximate the classical problem. In particular we obta…
Multiplicity of positive solutions for a degenerate nonlocal problem with p-Laplacian
2021
Abstract We consider a nonlinear boundary value problem with degenerate nonlocal term depending on the L q -norm of the solution and the p-Laplace operator. We prove the multiplicity of positive solutions for the problem, where the number of solutions doubles the number of “positive bumps” of the degenerate term. The solutions are also ordered according to their L q -norms.
Heat transfer in conducting and radiating bodies
1997
Abstract We introduce briefly some nonlocal models for heat transfer in conducting and radiating media. The goal is to give an idea of the general mathematical structure and related existence results for such models.