Nittka's invariance criterion and Hilbert space valued parabolic equations in $L_p$
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913271062200320 |
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| author | Arendt, W. ter Elst, A. F. M. Sauter, M. |
| author_facet | Arendt, W. ter Elst, A. F. M. Sauter, M. |
| contents | Nittka gave an efficient criterion on a form defined on $L_2(Ω)$ 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~$L_2(Ω,H)$. 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 $1 < p_- < 2 < p_+ < \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13885 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nittka's invariance criterion and Hilbert space valued parabolic equations in $L_p$ Arendt, W. ter Elst, A. F. M. Sauter, M. Analysis of PDEs Functional Analysis 35B45, 35K15 46B20 Nittka gave an efficient criterion on a form defined on $L_2(Ω)$ 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~$L_2(Ω,H)$. 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 $1 < p_- < 2 < p_+ < \infty$. |
| title | Nittka's invariance criterion and Hilbert space valued parabolic equations in $L_p$ |
| topic | Analysis of PDEs Functional Analysis 35B45, 35K15 46B20 |
| url | https://arxiv.org/abs/2310.13885 |