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| Main Authors: | , |
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| Format: | Preprint |
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2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.14197 |
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| _version_ | 1866910887136198656 |
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| author | Liu, Bingyuan Straube, Emil J. |
| author_facet | Liu, Bingyuan Straube, Emil J. |
| contents | Let $Ω$ be a smooth bounded pseudoconvex domain in $\mathbb{C}^{n}$. Let $1\leq q_{0}\leq (n-1)$. We show that if $q_{0}$--sums of eigenvalues of the Levi form are comparable, then if the Diederich--Fornæss index of $Ω$ is $1$, the $\overline{\partial}$--Neumann operators $N_{q}$ and the Bergman projections $P_{q-1}$ are regular in Sobolev norms for $q_{0}\leq q\leq n$. In particular, for domains in $\mathbb{C}^{2}$, Diederich--Fornæss index $1$ implies global regularity in the $\overline{\partial}$--Neumann problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_14197 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Diederich--Fornæss index and global regularity in the $\overline{\partial}$--Neumann problem: domains with comparable Levi eigenvalues Liu, Bingyuan Straube, Emil J. Complex Variables Let $Ω$ be a smooth bounded pseudoconvex domain in $\mathbb{C}^{n}$. Let $1\leq q_{0}\leq (n-1)$. We show that if $q_{0}$--sums of eigenvalues of the Levi form are comparable, then if the Diederich--Fornæss index of $Ω$ is $1$, the $\overline{\partial}$--Neumann operators $N_{q}$ and the Bergman projections $P_{q-1}$ are regular in Sobolev norms for $q_{0}\leq q\leq n$. In particular, for domains in $\mathbb{C}^{2}$, Diederich--Fornæss index $1$ implies global regularity in the $\overline{\partial}$--Neumann problem. |
| title | Diederich--Fornæss index and global regularity in the $\overline{\partial}$--Neumann problem: domains with comparable Levi eigenvalues |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2207.14197 |