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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.11522 |
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| _version_ | 1866912124949757952 |
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| author | Lamy, Xavier Marconi, Elio |
| author_facet | Lamy, Xavier Marconi, Elio |
| contents | We consider entropy solutions to the eikonal equation $|\nabla u|=1$ in two space dimensions. These solutions are motivated by a class of variational problems and fail in general to have bounded variation. Nevertheless they share with BV functions, several of their fine properties: we show in particular that the set of non-Lebesgue points has co-dimension at least one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_11522 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Lebesgue points of entropy solutions to the eikonal equation Lamy, Xavier Marconi, Elio Analysis of PDEs 35L60 We consider entropy solutions to the eikonal equation $|\nabla u|=1$ in two space dimensions. These solutions are motivated by a class of variational problems and fail in general to have bounded variation. Nevertheless they share with BV functions, several of their fine properties: we show in particular that the set of non-Lebesgue points has co-dimension at least one. |
| title | On Lebesgue points of entropy solutions to the eikonal equation |
| topic | Analysis of PDEs 35L60 |
| url | https://arxiv.org/abs/2211.11522 |