Precise subelliptic estimates for a class of special domains

Abstract

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

9 pages

References in corpus (2)

• Subellipticity of the $\bar{\partial }$-Neumann problem on a weakly $q$-pseudoconvex/concave domain
• Sharp Estimates for the $\bar{\partial }$-Neumann Problem on Regular Coordinate Domains