Fourth-order operators with unbounded coefficients in $L^1$ spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912660139802624 |
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| author | Gregorio, Federica Spina, Chiara Tacelli, Cristian |
| author_facet | Gregorio, Federica Spina, Chiara Tacelli, Cristian |
| contents | We prove that operators of the form $A=-a(x)^2Δ^{2}$, with suitable growth conditions on the coefficient $a(x)$, generate analytic semigroups in $L^1(\mathbb{R}^N)$. In particular, we deduce generation results for the operator $A :=- (1+|x|^2)^α Δ^{2}$, $0\leqα\leq2$. Moreover, we characterise the maximal domain of $A$ in $L^1(\mathbb{R}^N)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10551 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fourth-order operators with unbounded coefficients in $L^1$ spaces Gregorio, Federica Spina, Chiara Tacelli, Cristian Functional Analysis We prove that operators of the form $A=-a(x)^2Δ^{2}$, with suitable growth conditions on the coefficient $a(x)$, generate analytic semigroups in $L^1(\mathbb{R}^N)$. In particular, we deduce generation results for the operator $A :=- (1+|x|^2)^α Δ^{2}$, $0\leqα\leq2$. Moreover, we characterise the maximal domain of $A$ in $L^1(\mathbb{R}^N)$. |
| title | Fourth-order operators with unbounded coefficients in $L^1$ spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2407.10551 |