Hypoellipticity of the di-bar-Neumann problem at a set of infinite type with positive CR dimension
Luca Baracco, Stefano Pinton, Giuseppe Zampieri
TL;DR
This paper investigates the hypoellipticity of the di-bar-Neumann problem on certain domains with Levi-degeneracy, showing hypoellipticity without superlogarithmic estimates in positive CR dimension settings.
Contribution
It introduces a class of domains where the Kohn Laplacian is hypoelliptic but not superlogarithmic, with Levi-degeneracy points of positive CR dimension.
Findings
Hypoellipticity achieved without superlogarithmic estimates
Existence of Levi-degeneracy points with positive CR dimension
New domain classes with specific hypoelliptic properties
Abstract
This paper presents a class of domains on which the Kohn Laplacian and the dib-bar-Neumann problem are hypoelliptic but not superlogarithmic and which, moreover, have a set of points of Levi-degeneracy with positive CR dimension.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Spectral Theory in Mathematical Physics