The De Giorgi method for local and nonlocal systems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909161978068992 |
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| author | Behn, Linus Diening, Lars Nowak, Simon Scharle, Toni |
| author_facet | Behn, Linus Diening, Lars Nowak, Simon Scharle, Toni |
| contents | We extend the De Giorgi iteration technique to the vectorial setting. For this we replace the usual scalar truncation operator by a vectorial shortening operator. As an application, we prove local boundedness for local and nonlocal nonlinear systems. Furthermore, we show convex hull properties, which are a generalization of the maximum principle to the case of systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The De Giorgi method for local and nonlocal systems Behn, Linus Diening, Lars Nowak, Simon Scharle, Toni Analysis of PDEs 35D30, 35B45, 35B50, 35J60, 35R09 We extend the De Giorgi iteration technique to the vectorial setting. For this we replace the usual scalar truncation operator by a vectorial shortening operator. As an application, we prove local boundedness for local and nonlocal nonlinear systems. Furthermore, we show convex hull properties, which are a generalization of the maximum principle to the case of systems. |
| title | The De Giorgi method for local and nonlocal systems |
| topic | Analysis of PDEs 35D30, 35B45, 35B50, 35J60, 35R09 |
| url | https://arxiv.org/abs/2404.04063 |