Electron. J. Diff. Equ., Vol. 2016 (2016), No. 130, pp. 1-7.

Uniqueness of a positive solution for quasilinear elliptic equations in Heisenberg group

Kaushik Bal

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 $C^{1,\alpha}$ regularity for all $1<p<\infty$ is the problem to extend the proof of Diaz-Saa [10] 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
email: kaushik@iitk.ac.in

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