The Kato problem and extensions for degenerate elliptic operators of higher order in weighted spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909889743290368 |
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| author | Zhang, Guoming |
| author_facet | Zhang, Guoming |
| contents | We consider the Kato problem and extensions for degenerate elliptic operators of arbitrary order $2m$ ($m\geq 1$), whose coefficients are measurable, complex-valued and satisfy the G$\mathring{a}$rding inequality with respect to a Muckenhoupt $A_{2}$-weight; this generalizes the work of [Cruz-Uribe, Martell and Rios 2018]. As an application, the unweighted $L^{p}$-Dirichlet, regularity and Neumann boundary value problems associated to such an operator are solved when $p$ is sufficiently close to $2.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04046 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Kato problem and extensions for degenerate elliptic operators of higher order in weighted spaces Zhang, Guoming Analysis of PDEs We consider the Kato problem and extensions for degenerate elliptic operators of arbitrary order $2m$ ($m\geq 1$), whose coefficients are measurable, complex-valued and satisfy the G$\mathring{a}$rding inequality with respect to a Muckenhoupt $A_{2}$-weight; this generalizes the work of [Cruz-Uribe, Martell and Rios 2018]. As an application, the unweighted $L^{p}$-Dirichlet, regularity and Neumann boundary value problems associated to such an operator are solved when $p$ is sufficiently close to $2.$ |
| title | The Kato problem and extensions for degenerate elliptic operators of higher order in weighted spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.04046 |