Variational characterization of the regularity of Monge-Brenier maps
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arXiv
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| Format: | Preprint |
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2017
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| _version_ | 1866912000136708096 |
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| author | Ustunel, Ali Suleyman |
| author_facet | Ustunel, Ali Suleyman |
| contents | On an abstract Wiener space, assume that T is the solution of the quadratic Monge problem associated to the Wiener measure and a second one with a Radon-Nikodym derivative of exponential type. Under the finite information hypothesis, using a variational method, we prove that T minimizes a certain functional originating from the large deviations theory. Applying a variational method a la Euler, we obtain the Sobolev regularity of the backward Monge-Brenier map. A similar result also holds for the forward Monge-Brenier map. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1704_00310 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Variational characterization of the regularity of Monge-Brenier maps Ustunel, Ali Suleyman Probability 60H, 35Q On an abstract Wiener space, assume that T is the solution of the quadratic Monge problem associated to the Wiener measure and a second one with a Radon-Nikodym derivative of exponential type. Under the finite information hypothesis, using a variational method, we prove that T minimizes a certain functional originating from the large deviations theory. Applying a variational method a la Euler, we obtain the Sobolev regularity of the backward Monge-Brenier map. A similar result also holds for the forward Monge-Brenier map. |
| title | Variational characterization of the regularity of Monge-Brenier maps |
| topic | Probability 60H, 35Q |
| url | https://arxiv.org/abs/1704.00310 |