Diederich--Forn\ae ss index and global regularity in the $\overline{\partial}$--Neumann problem: domains with comparable Levi eigenvalues
| Autor: | Liu, Bingyuan, Straube, Emil J. |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $\Omega$ 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--Forn\ae ss index of $\Omega$ 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--Forn\ae ss index $1$ implies global regularity in the $\overline{\partial}$--Neumann problem. Comment: 16 pages |
| Databáze: | arXiv |
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