Asian Journal of Mathematics

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

Luca Baracco, Tran Vu Khanh, and Giuseppe Zampieri

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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 "A general method of weights in the $\overline{\partial}$-Neumann problem," [T. V. Khanh, Ph.D. Thesis, Padua (2009)].

Article information

Source
Asian J. Math., Volume 18, Number 4 (2014), 623-632.

Dates
First available in Project Euclid: 6 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1415284981

Mathematical Reviews number (MathSciNet)
MR3275722

Zentralblatt MATH identifier
1305.43006

Subjects
Primary: 32F10: $q$-convexity, $q$-concavity 32F20 32N15: Automorphic functions in symmetric domains 32T25: Finite type domains

Keywords
Hypoellipticity $\overline{\partial}$-Neumann superlogarithmic estimate infinite type

Citation

Baracco, Luca; Khanh, Tran Vu; Zampieri, Giuseppe. Hypoellipticity of the $\overline{\partial}$-Neumann problem at a point of infinite type. Asian J. Math. 18 (2014), no. 4, 623--632. https://projecteuclid.org/euclid.ajm/1415284981


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