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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2501.04532 |
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| _version_ | 1866917152714391552 |
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| author | Arendt, Wolfgang Sauter, Manfred |
| author_facet | Arendt, Wolfgang Sauter, Manfred |
| contents | We consider autonomous and non-autonomous evolution equations on a time interval $[0,τ]$ in a Banach space $X$ with the non-standard time-boundary condition $u(0)=Φu(τ)$, where $Φ$ is a linear map on $X$. If $Φ=0$, this is an initial value problem, whereas $Φ=I$ corresponds to periodic boundary conditions, and $Φ=-I$ to antiperiodic boundary conditions. Our main point is to establish maximal $L^p$-regularity. In the non-autonomous case we consider two situations. The first concerns time-dependent operators with a fixed domain. In the second one we take $X=H$ a Hilbert space and consider evolution equations associated with non-autonomous forms. Of special interest is then maximal regularity in $H$ with a non-standard time-boundary condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04532 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal regularity for generalized boundary conditions in time Arendt, Wolfgang Sauter, Manfred Analysis of PDEs Functional Analysis Primary: 35K90, Secondary: 35B65, 35B30, 47A07, 34G10 We consider autonomous and non-autonomous evolution equations on a time interval $[0,τ]$ in a Banach space $X$ with the non-standard time-boundary condition $u(0)=Φu(τ)$, where $Φ$ is a linear map on $X$. If $Φ=0$, this is an initial value problem, whereas $Φ=I$ corresponds to periodic boundary conditions, and $Φ=-I$ to antiperiodic boundary conditions. Our main point is to establish maximal $L^p$-regularity. In the non-autonomous case we consider two situations. The first concerns time-dependent operators with a fixed domain. In the second one we take $X=H$ a Hilbert space and consider evolution equations associated with non-autonomous forms. Of special interest is then maximal regularity in $H$ with a non-standard time-boundary condition. |
| title | Maximal regularity for generalized boundary conditions in time |
| topic | Analysis of PDEs Functional Analysis Primary: 35K90, Secondary: 35B65, 35B30, 47A07, 34G10 |
| url | https://arxiv.org/abs/2501.04532 |