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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.04532 |
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Table of 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.