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

Abstract

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.

Keywords

• Quasilinear elliptic equation
• Picone's identity
• Heisenberg group