Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2022; 59(3): 635-648

Published online May 1, 2022 https://doi.org/10.4134/JKMS.j210462

Copyright © The Korean Mathematical Society.

A Neumann type problem on an unbounded domain in the Heisenberg group

Shivani Dubey, Mukund Madhav Mishra, Ashutosh Pandey

University of Delhi; University of Delhi; University of Delhi

Abstract

We discuss the wellposedness of the Neumann problem on a half-space for the Kohn-Laplacian in the Heisenberg group. We then construct the Neumann function and explicitly represent the solution of the associated inhomogeneous problem.

Keywords: Neumann problem, Heisenberg group, sub-Laplacian, horizontal normal vectors, Neumann function

MSC numbers: 31B20, 35H20, 35N15, 45B05, 65N80

Supported by: The research is supported by the Senior Research Fellowship of Council of Scientific \& Industrial Research (CSIR), Government of India under grant reference number 09/045(1479)/2017-EMR-I.