The convexity of a planar domain via properties of solutions to the modified Helmholtz equation
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866914729142779904 |
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| author | Kuznetsov, Nikolay |
| author_facet | Kuznetsov, Nikolay |
| contents | A new characterization of convexity of a planar domain is obtained. Its derivation involves two classical facts: the Varadhan's formula, expressing the distance function with respect to the domain's boundary via real-valued solutions of the modified Helmholtz equation, and the convexity of a planar domain in which the distance function is superharmonic |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09382 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The convexity of a planar domain via properties of solutions to the modified Helmholtz equation Kuznetsov, Nikolay Analysis of PDEs A new characterization of convexity of a planar domain is obtained. Its derivation involves two classical facts: the Varadhan's formula, expressing the distance function with respect to the domain's boundary via real-valued solutions of the modified Helmholtz equation, and the convexity of a planar domain in which the distance function is superharmonic |
| title | The convexity of a planar domain via properties of solutions to the modified Helmholtz equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.09382 |