Liouville theorem for a class semilinear elliptic problem on Heisenberg group

TL;DR

This paper proves a Liouville theorem for a class of semilinear elliptic equations on the Heisenberg group, providing key estimates and extending classical results to a subcritical setting.

Contribution

It introduces a Liouville theorem for semilinear subcritical elliptic equations on the Heisenberg group, using a generalized integral estimate approach.

Findings

Established a Liouville theorem for the Heisenberg group

Derived a pointwise estimate near singularities

Developed an a priori integral estimate based on Jerison and Lee's formula

Abstract

We obtain an entire Liouville type theorem to the classical semilinear subcritical elliptic equation on Heisenberg group. A pointwise estimate near the isolated singularity was also proved. The soul of the proofs is an a priori integral estimate, which deduced from a generalized formula of that found by Jerison and Lee.