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Boundary regularity for the\(\bar \partial _b - Neumann\) problem, part 1problem, part 1

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Abstract

We establish sharp regularity and Fredholm theorems for the\(\bar \partial _b - Neumann\) operator on domains satisfying some nongeneric geometric conditions. We use these domains to construct explicit examples of bad behavior 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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Authors and Affiliations

  1. Department of Mathematics, Dartmouth College, 03755, Hanover, NH

    Robert K. Hladky

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  1. Robert K. Hladky
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Correspondence to Robert K. Hladky.

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Communicated by Steven Bell

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Hladky, R.K. Boundary regularity for the\(\bar \partial _b - Neumann\) problem, part 1problem, part 1. J Geom Anal 16, 117–153 (2006). https://doi.org/10.1007/BF02930989

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  • DOI: https://doi.org/10.1007/BF02930989

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