A Compactness Theorem for functions on Poisson point clouds

2022/05/11 by Marco Caroccia, Caroccia, Marco
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Approximation and Integration #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2205.05465

openalex publication_date 2022/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we show a compactness Theorem for discrete functions on Poisson point clouds. We consider sequences with equibounded non-local p-Dirichlet energy: the novelty consists in the intermediate-interaction regime at which the non-local energy is computed.

Related

• A generalization of Poletsky's classical theorem and a characterization of thinness of a subset in \Cⁿ
• Poisson structures with compact support
• Energy image density property and the lent particle method for Poisson measures
• An overview on the local limit of non-local conservation laws, and a new proof of a compactness estimate
• L^p compactness criteria with an application to variational convergence of some nonlocal energy functionals