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On Kac's principle of not feeling the boundary for the Kohn Laplacian on the Heisenberg group

Authors: Michael Ruzhansky and Durvudkhan Suragan
Journal: Proc. Amer. Math. Soc. 144 (2016), 709-721
MSC (2010): Primary 35R03, 35S15
Published electronically: June 26, 2015
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Abstract: In this note we construct an integral boundary condition for the Kohn Laplacian in a given domain on the Heisenberg group extending to the setting of the Heisenberg group M. Kac's ``principle of not feeling the boundary''. This also amounts to finding the trace on smooth surfaces of the Newton potential associated to the Kohn Laplacian. We also obtain similar results for higher powers of the Kohn Laplacian.

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Additional Information

Michael Ruzhansky
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom

Durvudkhan Suragan
Affiliation: Institute of Mathematics and Mathematical Modelling, 125 Pushkin Str., 050010 Almaty, Kazakhstan

Keywords: Sub-Laplacian, Kohn Laplacian, integral boundary conditions, Heisenberg group, Newton potential
Received by editor(s): January 26, 2015
Published electronically: June 26, 2015
Additional Notes: The authors were supported in part by EPSRC grant EP/K039407/1 and by the Leverhulme grant RPG-2014-02, as well as by MESRK grant 5127/GF4.
Communicated by: Joachim Krieger
Article copyright: © Copyright 2015 American Mathematical Society