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arXiv · 2310.13885

Nittka's invariance criterion and Hilbert space valued parabolic equations in $L_p$

W. Arendt·A. F. M. ter Elst·M. Sauter
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Abstract

Nittka gave an efficient criterion on a form defined on $L_2(\Omega)$ which implies that the associated semigroup is $L_p$-invariant for some given $p \in (1,\infty)$. We extend this criterion to the Hilbert space valued~$L_2(\Omega,H)$. As an application we consider elliptic systems of pure second order. Our main result shows that the induced semigroup is $L_p$-contractive for all $p \in [p_-,p_+]$ for some $1 < p_- < 2 < p_+ < \infty$.

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W. Arendt, A. F. M. ter Elst, M. Sauter. 2023-10-21. Nittka's invariance criterion and Hilbert space valued parabolic equations in $L_p$. https://doi.org/10.1007/s00013-023-01944-0

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