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

Robert K. Hladky
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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.

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Robert K. Hladky. 2004-12-15. Boundary Regularity for the \bar{\partial}_b-Neumann Problem, Part 1. https://arxiv.org/abs/math/0412308

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