Asian Journal of Mathematics

Volume 18 (2014)

Number 4

Hypoellipticity of the $\overline{\partial}$-Neumann problem at a point of infinite type

Pages: 623 – 632

DOI: https://dx.doi.org/10.4310/AJM.2014.v18.n4.a4

Authors

Luca Baracco (Dipartimento di Matematica, Università di Padova, Italy)

Tran Vu Khanh (Department of Mathematics, National University of Singapore)

Giuseppe Zampieri (Dipartimento di Matematica, Università di Padova, Italy)

Abstract

We prove local hypoellipticity of the complex Laplacian $\square$ in a domain which has superlogarithmic estimates outside a curve transversal to the CR directions and for which the holomorphic tangential derivatives of a defining function are superlogarithmic multipliers in the sense of [10].

Keywords

hypoellipticity, $\overline{\partial}$-Neumann problem, superlogarithmic estimate, infinite type

2010 Mathematics Subject Classification

32F10, 32N15, 32T25

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Published 4 November 2014