On the doubling of variables technique in first order Hamilton-Jacobi equations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917121938685952 |
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| author | Bertucci, Charles Silberstein, Giacomo Ceccherini |
| author_facet | Bertucci, Charles Silberstein, Giacomo Ceccherini |
| contents | In this paper, we revisit the technique of doubling variables in first order Hamilton-Jacobi equations, especially when the equations arise in optimal control. We show that by tuning the penalization between the two points, we can change drastically the proof, somehow shifting the regularity hypotheses into geometrical properties of the penalization. We present this idea in a finite dimensional setting and then exploit it on equations posed on Wasserstein spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03652 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the doubling of variables technique in first order Hamilton-Jacobi equations Bertucci, Charles Silberstein, Giacomo Ceccherini Analysis of PDEs In this paper, we revisit the technique of doubling variables in first order Hamilton-Jacobi equations, especially when the equations arise in optimal control. We show that by tuning the penalization between the two points, we can change drastically the proof, somehow shifting the regularity hypotheses into geometrical properties of the penalization. We present this idea in a finite dimensional setting and then exploit it on equations posed on Wasserstein spaces. |
| title | On the doubling of variables technique in first order Hamilton-Jacobi equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.03652 |