Regularity of the $\bar\partial$-Neumann problem by means of superlogarithmic multipliers
Complex Variables
2014-12-16 v1
Abstract
This thesis starts from a review on current research on the local hypoellipticity of the -Neumann problem. It presents the classical method of regularity from estimates of the energy: subelliptic as well as superlogarithmic. More recent material is included in which the regularity of the solution is obtained from the geometry of the singularities of the Levi form. The new contribution to this discussion consists in a general weighted Kohn-H\"ormander-Morrey formula twisted by a pseudodifferential operator. As an application, a new class of domains for which the -Neumann problem is locally regular is exhibited.
Keywords
Cite
@article{arxiv.1412.4156,
title = {Regularity of the $\bar\partial$-Neumann problem by means of superlogarithmic multipliers},
author = {Martino Fassina},
journal= {arXiv preprint arXiv:1412.4156},
year = {2014}
}
Comments
A thesis submitted for the Master's Degree in Mathematics at the University of Padova