Interior regularity of optimal transport paths
type: Item
instance of: scholarly article
title: Interior regularity of optimal transport paths
zbMATH Open document ID: 1080.90008
author: Qinglan Xia
published in: Calculus of Variations and Partial Differential Equations
publication date: 2004-12-16T00:00:00Z
review text: Optimal transport paths arise in one of the many variants of the mass transport problem. Precisely the author consider a mass transport problem for which the cost of transport depends on the actual transport path rather then on the distance between the original and the final location of the mass. In this paper transport paths are real flat 1-chains and the associated cost is given by the \(M^\alpha\)-mass (extended from polyhedral chains) for some \(\alpha \in [0,1]\). In a previous paper the author proved that a real flat \(k\)-chain with finite \(M^\alpha\)-mass is rectifiable. In this paper first a tangent cone property is introduced for optimal transport paths. Then it is proved that near an interior point a local finiteness property holds. It follows that near an interior point and optimal transport path is a finite union of segments.
reviewed by: Luigi De Pascale
Mathematics Subject Classification ID: 90B06
Mathematics Subject Classification ID: 49Q20
zbMATH DE Number: 2123231
zbMATH Keywords: optimal transport path
zbMATH Keywords: real flat chains
MaRDI profile type: Publication
full work available at URL: s00526-003-0237-6
OpenAlex ID: W2010491857
DOI: 10.1007/S00526-003-0237-6
description: scientific article; zbMATH DE number 2123231