The divergence theorem and nonlocal counterparts
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916147019907072 |
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| author | Hepp, Solveig Kassmann, Moritz |
| author_facet | Hepp, Solveig Kassmann, Moritz |
| contents | We present a new proof of the classical divergence theorem in bounded domains. Our proof is based on a nonlocal analog of the divergence theorem and a rescaling argument. Main ingredients in the proof are nonlocal versions of the divergence and the normal derivative. We employ these to provide definitions of well-known nonlocal concepts such as the fractional perimeter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_01945 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The divergence theorem and nonlocal counterparts Hepp, Solveig Kassmann, Moritz Analysis of PDEs 26B20, 35R09, 47G20 We present a new proof of the classical divergence theorem in bounded domains. Our proof is based on a nonlocal analog of the divergence theorem and a rescaling argument. Main ingredients in the proof are nonlocal versions of the divergence and the normal derivative. We employ these to provide definitions of well-known nonlocal concepts such as the fractional perimeter. |
| title | The divergence theorem and nonlocal counterparts |
| topic | Analysis of PDEs 26B20, 35R09, 47G20 |
| url | https://arxiv.org/abs/2302.01945 |