Uniqueness and comparison principles for semilinear equations and inequalities in Carnot groups

Abstract

Variants of the Kato inequality are proved for distributional solutions of semilinear equations and inequalities on Carnot groups. Various applications to uniqueness, comparison of solutions and Liouville theorems are presented.

Keywords

• kato inequality
• comparison principles
• uniqueness property
• semilinear inequalities
• liouville theorems
• carnot groups
• 35r03
• 35r45
• 35a05
• 35b51