Boundary Regularity for the \bar{\partial}_b-Neumann Problem, Part 1

Robert K. Hladky

Boundary Regularity for the \bar{\partial}_b-Neumann Problem, Part 1

Complex Variables 2007-05-23 v1 Differential Geometry

Authors: Robert K. Hladky

Abstract

We establish sharp regularity and Fredholm theorems for the \bar{\partial}_b-Neumann problem on domains satisfying some non-generic geometric conditions. We use these domains to construct explicit examples of bad behaviour of the Kohn Laplacian: it is not always hypoelliptic up to the boundary, its partial inverse is not compact and it is not globally subelliptic.

Keywords

regularity for elliptic equations fractional laplacian boundary value problems

Cite

@article{arxiv.math/0412308,
  title  = {Boundary Regularity for the \bar{\partial}_b-Neumann Problem, Part 1},
  author = {Robert K. Hladky},
  journal= {arXiv preprint arXiv:math/0412308},
  year   = {2007}
}