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arXiv · 1612.07446

The Kohn-Laplace equation on abstract CR manifolds: Local regularity

Tran Vu Khanh
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Abstract

The purpose of this paper is to establish local regularity of the solution operator to the Kohn-Laplace equation, called the complex Green operator, on abstract CR manifolds of hypersurface type. For a cut-off function $\sigma$, we introduce the $\sigma$-superlogarithmic property, a potential theoretical condition on CR manifolds. We prove that if the given datum is smooth on an open set containing the support of $\sigma$ then the solution is smooth on the interior of $\{x\in M:\sigma(x)=1\}$. Furthermore, we also study the smoothness of the integral kernel of the complex Green operator.

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Tran Vu Khanh. 2016-12-22. The Kohn-Laplace equation on abstract CR manifolds: Local regularity. https://arxiv.org/abs/1612.07446

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