PARTIAL REGULARITY FOR OPTIMAL TRANSPORT WITH p-COST AWAY FROM FIXED POINTS

Michael Goldman; Lukas Koch

doi:10.1090/proc/17285

PARTIAL REGULARITY FOR OPTIMAL TRANSPORT WITH p-COST AWAY FROM FIXED POINTS

Michael Goldman
, Lukas Koch

University of Sussex

Research output: Contribution to journal › Article › peer-review

Abstract

We consider maps T solving the optimal transport problem with a cost c(x − y) modeled on the p-cost. For Hölder continuous marginals, we prove a C^1,α-partial regularity result for T in the set {|T(x) − x| > 0}.

Original language	English
Pages (from-to)	3959-3970
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	153
Issue number	9
DOIs	https://doi.org/10.1090/proc/17285
Publication status	Published - 1 Sept 2025

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title = "PARTIAL REGULARITY FOR OPTIMAL TRANSPORT WITH p-COST AWAY FROM FIXED POINTS",

abstract = "We consider maps T solving the optimal transport problem with a cost c(x − y) modeled on the p-cost. For H{\"o}lder continuous marginals, we prove a C1,α-partial regularity result for T in the set \{|T(x) − x| > 0\}.",

author = "Michael Goldman and Lukas Koch",

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AB - We consider maps T solving the optimal transport problem with a cost c(x − y) modeled on the p-cost. For Hölder continuous marginals, we prove a C1,α-partial regularity result for T in the set {|T(x) − x| > 0}.

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JO - Proceedings of the American Mathematical Society

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PARTIAL REGULARITY FOR OPTIMAL TRANSPORT WITH p-COST AWAY FROM FIXED POINTS

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