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Author ORCID Identifier
https://orcid.org/0000-0003-2315-7505
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
Year Degree Awarded
2022
Month Degree Awarded
May
First Advisor
Nestor Guillen
Subject Categories
Analysis
Abstract
In this work we study a modification of the Monge-Kantorovich problem taking into account path dependence and interaction effects between particles. We prove existence of solutions under mild conditions on the data, and after imposing stronger conditions, we characterize the minimizers by relating them to an auxiliary Monge-Kantorovich problem of the more standard kind. With this notion of how particles interact and travel along paths, we produce a dual problem. The main novelty here is to incorporate an interaction effect to the optimal path transport problem. This covers for instance, N-body dynamics when the underlying measures are discrete. Lastly, our results include an extension of Brenier's theorem on optimal transport maps.
DOI
https://doi.org/10.7275/28635013
Recommended Citation
Cabrera, Rene, "AN OPTIMAL TRANSPORTATION THEORY FOR INTERACTING PATHS" (2022). Doctoral Dissertations. 2504.
https://doi.org/10.7275/28635013
https://scholarworks.umass.edu/dissertations_2/2504
Creative Commons License
This work is licensed under a Creative Commons Attribution-Share Alike 4.0 License.