Subellipticity of the $\bar\partial$-Neumann problem on a weakly $q$-pseudoconvex/concave domain

A sufficient condition for subellipticity of the d-bar-Neumann operator

We give a sufficient condition for subelliptic estimates for the d-bar-Neumann operator on smoothly bounded, pseudoconvex domains in $\mathbb{C}^n$. This condition is a quantified version of McNeal's condition ($\tilde{P}$) for compactness of the d-bar-Neumann operator, and it extends Catlin's condition for subellipticity as it is less stringent.

Algorithms for subelliptic multipliers in $\mathbb{C}^2$

We give examples of pseudoconvex domains of finite type in $\mathbb{C}^2$ where the Kohn algorithm for subelliptic estimates fails to yield an effective lower bound for the order of subellipticity in terms of the type. We show how to modify the algorithm to obtain an effective procedure to prove subellipticity on domains of finite type in $\mathbb{C}^2$ with real analytic boundary satisfying a condition slightly stronger than pseudoconvexity. We close with a generalization to higher dimensions.

Superlogarithmic estimates on pseudoconvex domains and CR manifolds

This paper is concerned with proving superlogarithmic estimates for the operator $\Box_b$ on pseudoconvex CR manifolds and using them to establish hypoellipticity of $\Box_b$ and of the $\bar{\partial}$-Neumann problem. These estimates are established under the assumption that subellipticity degenerates in certain specified ways.

$\mathbb{C}$-凸域上的Gromov双曲性、有限型和次椭圆性

Gromov hyperbolicity, finite type, and subellipticity on $\mathbb{C}$-convex domains

本文证明有界光滑$\mathbb{C}$-凸域的Kobayashi距离Gromov双曲性、D'Angelo型有限性与$\bar{\partial}$-Neumann问题次椭圆估计三者等价，并给出相关指数与边界等价性结果。