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arXiv · 0812.2560

Precise subelliptic estimates for a class of special domains

Tran Vu Khanh·Giuseppe Zampieri
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Abstract

For the $\bar\partial$-Neumann problem on a regular coordinate domain $Ω\subset \C^{n+1}$, we prove $ε$-subelliptic estimates for an index $ε$ which is in some cases better than $ε=\frac1{2m}$ ($m$ being the {\it multiplicity}) as it was previously proved by Catlin and Cho in \cite{CC08}. This also supplies a much simplified proof of the existing literature. Our approach is founded on the method by Catlin in \cite{C87} which consists in constructing a family of weights $\{ϕ^δ\}$ whose Levi form is bigger than $δ^{-2ε}$ on the $δ$-strip around $\partialΩ$.

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Tran Vu Khanh, Giuseppe Zampieri. 2009-01-07. Precise subelliptic estimates for a class of special domains. https://arxiv.org/abs/0812.2560

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