Publication 15-CNA-014

On The Regularity Of The Free Boundary In The Ooptimal Partial Transport Problem For General Cost Functions

Shibing Chen
Department of Mathematics
Zhejiang University of Technology
Hangzhou 310023, China
schen@zjtu.edu.cn

E. Indrei
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA
egi@cmu.edu

Abstract: This paper concerns the regularity and geometry of the free boundary in the optimal partial transport problem for general cost functions. More specifically, we prove that a C1 cost implies a locally Lipschitz free boundary. As an application, we address a problem discussed by Caffarelli and McCann [1] regarding cost functions satisfying the Ma-Trudinger-Wang condition (A3). Furthermore, we show that a locally Lipschitz cost implies a rectifiable free boundary and initiate a corresponding regularity theory in the Riemannian setting.

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