Aubry Set of Eikonal Hamilton-Jacobi Equations on Networks
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908387209379840 |
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| author | Pozza, Marco |
| author_facet | Pozza, Marco |
| contents | We extend the study of eikonal Hamilton-Jacobi equations posed on networks performed by Siconolfi and Sorrentino (Anal. PDE, 2018) to a more general setting. Their approach essentially exploits that such equations correspond to discrete problems on an abstract underlying graph. However, a specific condition they assume can be rather restricting in some settings, which motivates the generalization we propose. We still get an Aubry set, which plays the role of a uniqueness set for our problem and appears in the representation of solutions. Exploiting it we establish a new comparison principle between super and subsolutions to the equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_01625 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Aubry Set of Eikonal Hamilton-Jacobi Equations on Networks Pozza, Marco Analysis of PDEs 35F21, 35R02, 35B51, 49L25 We extend the study of eikonal Hamilton-Jacobi equations posed on networks performed by Siconolfi and Sorrentino (Anal. PDE, 2018) to a more general setting. Their approach essentially exploits that such equations correspond to discrete problems on an abstract underlying graph. However, a specific condition they assume can be rather restricting in some settings, which motivates the generalization we propose. We still get an Aubry set, which plays the role of a uniqueness set for our problem and appears in the representation of solutions. Exploiting it we establish a new comparison principle between super and subsolutions to the equation. |
| title | Aubry Set of Eikonal Hamilton-Jacobi Equations on Networks |
| topic | Analysis of PDEs 35F21, 35R02, 35B51, 49L25 |
| url | https://arxiv.org/abs/2412.01625 |