Elliptic operators with non-local Wentzell-Robin boundary conditions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| author | Kunze, Markus Mui, Jonathan Ploss, David |
| author_facet | Kunze, Markus Mui, Jonathan Ploss, David |
| contents | In this article, we study strictly elliptic, second-order differential operators on a bounded Lipschitz domain in $\mathbb{R}^d$, subject to certain non-local Wentzell-Robin boundary conditions. We prove that such operators generate strongly continuous semigroups on $L^2$-spaces and on spaces of continuous functions. We also provide a characterisation of positivity and (sub-)Markovianity of these semigroups. Moreover, based on spectral analysis of these operators, we discuss further properties of the semigroup such as asymptotic behaviour and, in the case of a non-positive semigroup, the weaker notion of eventual positivity of the semigroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03216 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elliptic operators with non-local Wentzell-Robin boundary conditions Kunze, Markus Mui, Jonathan Ploss, David Analysis of PDEs Functional Analysis Primary: 35J25, 35P05, Secondary: 35B40, 47D06, 35B09 In this article, we study strictly elliptic, second-order differential operators on a bounded Lipschitz domain in $\mathbb{R}^d$, subject to certain non-local Wentzell-Robin boundary conditions. We prove that such operators generate strongly continuous semigroups on $L^2$-spaces and on spaces of continuous functions. We also provide a characterisation of positivity and (sub-)Markovianity of these semigroups. Moreover, based on spectral analysis of these operators, we discuss further properties of the semigroup such as asymptotic behaviour and, in the case of a non-positive semigroup, the weaker notion of eventual positivity of the semigroup. |
| title | Elliptic operators with non-local Wentzell-Robin boundary conditions |
| topic | Analysis of PDEs Functional Analysis Primary: 35J25, 35P05, Secondary: 35B40, 47D06, 35B09 |
| url | https://arxiv.org/abs/2502.03216 |