The Wentzell Laplacian via forms and the approximative trace
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914205883432960 |
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| author | Arendt, Wolfgang Sauter, Manfred |
| author_facet | Arendt, Wolfgang Sauter, Manfred |
| contents | We use form methods to define suitable realisations of the Laplacian on a domain $Ω$ with Wentzell boundary conditions, i.e. such that $\partial_{\mathrm{n}}u + βu + Δu = 0$ holds in a suitable sense on the boundary of $Ω$. For those realisations, we study their semigroup generation properties. Using the approximative trace, we give a unified treatment that in part allows irregular and even fractal domains. Moreover, we admit $β$ to be merely essentially bounded and complex-valued. If the domain is Lipschitz, we obtain a kernel continuous up to the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_12981 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Wentzell Laplacian via forms and the approximative trace Arendt, Wolfgang Sauter, Manfred Analysis of PDEs Primary: 35J05, Secondary: 47D60, 31C25, 46E35 We use form methods to define suitable realisations of the Laplacian on a domain $Ω$ with Wentzell boundary conditions, i.e. such that $\partial_{\mathrm{n}}u + βu + Δu = 0$ holds in a suitable sense on the boundary of $Ω$. For those realisations, we study their semigroup generation properties. Using the approximative trace, we give a unified treatment that in part allows irregular and even fractal domains. Moreover, we admit $β$ to be merely essentially bounded and complex-valued. If the domain is Lipschitz, we obtain a kernel continuous up to the boundary. |
| title | The Wentzell Laplacian via forms and the approximative trace |
| topic | Analysis of PDEs Primary: 35J05, Secondary: 47D60, 31C25, 46E35 |
| url | https://arxiv.org/abs/2204.12981 |