A Liouville theorem for superlinear parabolic equations on the Heisenberg group

Abstract

We consider a parabolic nonlinear equation on the Heisenberg group. Applying the Gidas–Spruck type estimates, we prove that under suitable conditions, the equation does not have positive solutions. As an application of the nonexistence result, we provide optimal universal estimates for positive solutions.

Keywords

• heisenberg group
• liouville theorem
• blow up rate estimate
• parabolic nonlinear equation
• gidas–spruck type estimates
• primary 35k58, 35b09
• secondary 35j60