A smooth variational principle on Wasserstein space
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- by Erhan Bayraktar, Ibrahim Ekren and Xin Zhang;
- Proc. Amer. Math. Soc. 151 (2023), 4089-4098
- DOI: https://doi.org/10.1090/proc/16466
- Published electronically: May 25, 2023
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Abstract:
In this note, we provide a smooth variational principle on Wasserstein space by constructing a smooth gauge-type function using the sliced Wasserstein distance. This function is a crucial tool for optimization problems and in viscosity theory of PDEs on Wasserstein space.References
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Bibliographic Information
- Erhan Bayraktar
- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48103
- MR Author ID: 743030
- ORCID: 0000-0002-1926-4570
- Email: erhan@umich.edu
- Ibrahim Ekren
- Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32304
- MR Author ID: 1055795
- ORCID: 0000-0001-8649-2736
- Email: iekren@fsu.edu
- Xin Zhang
- Affiliation: Department of Mathematics, University of Vienna, 1090 Wien, Austria
- ORCID: 0000-0002-0036-5996
- Email: xin.zhang@univie.ac.at
- Received by editor(s): September 29, 2022
- Received by editor(s) in revised form: November 15, 2022, and February 9, 2023
- Published electronically: May 25, 2023
- Additional Notes: The first author was partially supported by the National Science Foundation under grant DMS-2106556 and by the Susan M. Smith chair.
The second author was supported in part by NSF Grant DMS 2007826. - Communicated by: Amarjit Budhiraja
- © Copyright 2023 by the authors
- Journal: Proc. Amer. Math. Soc. 151 (2023), 4089-4098
- MSC (2020): Primary 58E30, 90C05
- DOI: https://doi.org/10.1090/proc/16466
- MathSciNet review: 4607651