Properties of solutions to fractional p-subLaplace equations on the Heisenberg group

Abstract

Abstract The aim of this paper is to study properties of solutions to the fractional p-subLaplace equations on the Heisenberg group. Based on the maximum principles and the generalization of the direct method of moving planes, we obtain the symmetry and monotonicity of the solutions on the whole group and the Liouville property of solutions on a half space.

Keywords

• Fractional p-subLaplace equation
• Heisenberg group
• Maximum principle
• Direct method of moving planes