Hypoellipticity of the $\bar{\partial }$-Neumann problem by means of subelliptic multipliers

Abstract

We prove local hypoellipticity of the complex Laplacian $\square$ and of the Kohn Laplacian ${\square }_b$ in a pseudoconvex boundary when, for a system of cut-off $\eta$, the gradient ${\partial }_b\eta$ and the Levi form ${\partial }_b{\bar{\partial }}_b{\eta }^2$ are subelliptic multipliers in the sense of Kohn.

References in corpus (1)

• Propagation of regularity for solutions of the Kohn Laplacian in a flat boundary

Cited by in corpus (1)

• Local regularity of the Green operator in a CR manifold of general "type"