The boundary Harnack principle on optimal domains
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
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| _version_ | 1866911774323769344 |
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| author | Maiale, Francesco Paolo Tortone, Giorgio Velichkov, Bozhidar |
| author_facet | Maiale, Francesco Paolo Tortone, Giorgio Velichkov, Bozhidar |
| contents | We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that behaves as the distance function to the boundary, is subharmonic inside the domain and satisfies some suitable estimates on the measure of its level sets. We also discuss the applications of this result to some shape optimization and free boundary problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_01217 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The boundary Harnack principle on optimal domains Maiale, Francesco Paolo Tortone, Giorgio Velichkov, Bozhidar Analysis of PDEs 35R35, 49Q10 We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that behaves as the distance function to the boundary, is subharmonic inside the domain and satisfies some suitable estimates on the measure of its level sets. We also discuss the applications of this result to some shape optimization and free boundary problems. |
| title | The boundary Harnack principle on optimal domains |
| topic | Analysis of PDEs 35R35, 49Q10 |
| url | https://arxiv.org/abs/2112.01217 |