Abstract
We prove local hypoellipticity of the complex Laplacian \(\Box \) and of the Kohn Laplacian \(\Box _b\) in a pseudoconvex boundary when, for a system of cut-off \(\eta \), the gradient \(\partial _b\eta \) and the Levi form \(\frac{1}{2}(\partial _b\bar{\partial }_b-\bar{\partial }_b\partial _b)\eta \) are subelliptic multipliers in the sense of Kohn (Acta Math 142:79–122, 1979).
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Acknowledgments
The paper was accomplished at Sao Paulo USP in November 2013. The authors are grateful to Paulo Domingo Cordaro for friendly hospitality and fruitful discussions.
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Baracco, L., Pinton, S. & Zampieri, G. Hypoellipticity of the Kohn-Laplacian \(\Box _b\) and of the \(\bar{\partial }\)-Neumann problem by means of subelliptic multipliers. Math. Ann. 362, 887–901 (2015). https://doi.org/10.1007/s00208-014-1144-1
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DOI: https://doi.org/10.1007/s00208-014-1144-1