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$ \overline\partial$-equation on a lunar domain with mixed boundary conditions


Authors: Xiaojun Huang and Xiaoshan Li
Journal: Trans. Amer. Math. Soc. 368 (2016), 6915-6937
MSC (2010): Primary 32W05; Secondary 32V15
DOI: https://doi.org/10.1090/tran/6547
Published electronically: February 10, 2016
MathSciNet review: 3471081
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Abstract: In this paper, making use of the method developed by Catlin, we study the $ L^2$-estimate for the $ \bar \partial $-equation on a lunar manifold with mixed boundary conditions.


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Additional Information

Xiaojun Huang
Affiliation: School of Mathematics and Statistics, Wuhan University, Hubei 430072, People’s Republic of China – and – Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Email: huangx@math.rutgers.edu

Xiaoshan Li
Affiliation: School of Mathematics and Statistics, Wuhan University, Hubei 430072, People’s Republic of China
Email: xiaoshanli@whu.edu.cn

DOI: https://doi.org/10.1090/tran/6547
Keywords: $\overline\partial$-operator, $L^2$-estimate, $\overline\partial$-Dirichlet boundary condition, $\overline\partial$-Neumann boundary condition
Received by editor(s): March 4, 2014
Received by editor(s) in revised form: August 20, 2014
Published electronically: February 10, 2016
Additional Notes: The first author was supported in part by NSF-1363418
The second author was supported by the China Scholarship Council and the Fundamental Research Fund for the Central Universities
Article copyright: © Copyright 2016 American Mathematical Society