Symmetry for a quasilinear elliptic equation in Hyperbolic space

Abstract

In this article we establish the radial symmetry of positive solutions of a p- Laplace equation in the Hyperbolic space, which is the Euler Lagrange equation of the p- Poincare Sobolev inequality in the Hyperbolic space. We will also establish the sharp decay of solution and its gradient and also investigate the question of existence of solution.

arXiv commentAdded more details in proof of Theorem-3.8 and a new Remark-3.9. New Lemma-4.1 added. Corrected typos