Boundary Regularity for the ∂b-Neumann Problem, Part 1

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We establish sharp regularity and Fredholm theorems for the ∂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.