Sharp boundary ε-regularity of optimal transport maps

In this paper we develop a boundary ε-regularity theory for optimal transport maps between bounded open sets with C1,α-boundary. Our main result asserts sharp C1,α-regularity of transport maps at the boundary in form of a linear estimate under certain assumptions: The main quantitative assumptions a...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 381; p. 107603
Main Authors Miura, Tatsuya, Otto, Felix
Format Journal Article
LanguageEnglish
Published Elsevier Inc 16.04.2021
Subjects
Boundary regularity
Epsilon-regularity
Optimal transport
Boundary regularity
Optimal transport
Epsilon-regularity
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Summary:In this paper we develop a boundary ε-regularity theory for optimal transport maps between bounded open sets with C1,α-boundary. Our main result asserts sharp C1,α-regularity of transport maps at the boundary in form of a linear estimate under certain assumptions: The main quantitative assumptions are that the local nondimensionalized transport cost is small and that the boundaries are locally almost flat in C1,α. Our method is completely variational and builds on the recently developed interior regularity theory.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2021.107603