An isoperimetric result for an energy related to the $p$-capacity
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916198000623616 |
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| author | Acampora, Paolo Cristoforoni, Emanuele |
| author_facet | Acampora, Paolo Cristoforoni, Emanuele |
| contents | In this paper, we generalize the notion of relative $p$-capacity of $K$ with respect to $Ω$, by replacing the Dirichlet boundary condition with a Robin one. We show that, under volume constraints, our notion of $p$-capacity is minimal when $K$ and $Ω$ are concentric balls. We use the $H$-function and a derearrangement technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_14582 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An isoperimetric result for an energy related to the $p$-capacity Acampora, Paolo Cristoforoni, Emanuele Analysis of PDEs 35J66, 35J92, 35R35 In this paper, we generalize the notion of relative $p$-capacity of $K$ with respect to $Ω$, by replacing the Dirichlet boundary condition with a Robin one. We show that, under volume constraints, our notion of $p$-capacity is minimal when $K$ and $Ω$ are concentric balls. We use the $H$-function and a derearrangement technique. |
| title | An isoperimetric result for an energy related to the $p$-capacity |
| topic | Analysis of PDEs 35J66, 35J92, 35R35 |
| url | https://arxiv.org/abs/2207.14582 |