In this note we address the question of uniqueness of the Brezis-Oswald problem for the p-Laplacian operator in Heisenberg Group. The non-availability of regularity for all is the problem to extend the proof of Diaz-Saa  in the Heisenberg Group case. We overcome the problem by proving directly a generalized version of Diaz-Saa inequality in the Heisenberg Group.
Submitted January 18, 20016. Published June 6, 2016.
Math Subject Classifications: 35R03, 35J92, 35J70.
Key Words: Quasilinear elliptic equation; Picone's identity; Heisenberg group.
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| Kaushik Bal |
Department of Mathematics and Statistics
Indian Institute of Technology
Kanpur, Uttar Pradesh-280016 India
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