论文标题
deDerich-fornæss索引和全球规律性在$ \ edline {\ partial} $ - Neumann问题：具有可比Levi Eigenvalues的域名
Diederich--Fornæss index and global regularity in the $\overline{\partial}$--Neumann problem: domains with comparable Levi eigenvalues
论文作者
论文摘要
令$ω$为$ \ mathbb {c}^{n} $中的平滑有限的pseudoconvex域。令$ 1 \ leq q_ {0} \ leq（n-1）$。我们表明，如果$ q_ {0} $ - Levi表单的特征值总和是可比的，那么，如果Diederich-Fornæss$ω$的指数为$ 1 $，则$ \ operline {\ partial} $ - neumann operators $ n_ {q} $ nor n _ {q} $ projections $ p_ projections $ p _} $ q_ {0} \ leq q \ leq n $。特别是，对于$ \ mathbb {c}^{2} $中的域，diesterich-fornæss索引$ 1 $ $ 1 $表示$ \ overline {\ partial} $中的全局规律性 - neumann问题。
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.
