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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.14187 |
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| _version_ | 1866909149054369792 |
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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 $|D a(x)|\leq c a(x)^\frac{1}{2}$, generate analytic semigroups in $L^p(\mathbb{R}^N)$ for $1<p\leq\infty$ and in $C_b(\mathbb{R}^N)$. In particular, we deduce generation results for the operator $A :=- (1+|x|^2)^α Δ^{2}$, $0\leqα\leq2$. Moreover, we characterize the maximal domain of such operators in $L^p(\mathbb{R}^N)$ for $1<p<\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14187 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fourth-order operators with unbounded coefficients Gregorio, Federica Spina, Chiara Tacelli, Cristian Analysis of PDEs We prove that operators of the form $A=-a(x)^2Δ^{2}$, with $|D a(x)|\leq c a(x)^\frac{1}{2}$, generate analytic semigroups in $L^p(\mathbb{R}^N)$ for $1<p\leq\infty$ and in $C_b(\mathbb{R}^N)$. In particular, we deduce generation results for the operator $A :=- (1+|x|^2)^α Δ^{2}$, $0\leqα\leq2$. Moreover, we characterize the maximal domain of such operators in $L^p(\mathbb{R}^N)$ for $1<p<\infty$. |
| title | Fourth-order operators with unbounded coefficients |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.14187 |