Precise subelliptic estimates for a class of special domains

Details Precise subelliptic estimates for a class of special domains Precise subelliptic estimates for a class of special domains

2008-12-13

arxiv.org/abs/0812.2560v2

Mathematics

Complex Variables

9 pages

Scientific paper

For the $\bar\partial$-Neumann problem on a regular coordinate domain $\Omega\subset \C^{n+1}$, we prove $\epsilon$-subelliptic estimates for an index $\epsilon$ which is in some cases better than $\epsilon=\frac1{2m}$ ($m$ 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 $\{\phi^\delta\}$ whose Levi form is bigger than $\delta^{-2\epsilon}$ on the $\delta$-strip around $\partial\Omega$.

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