Barrier functions for Pucci Heisenberg operators and applications

Abstract

The aim of this paper is the explicit construction of some barrier functions ('fundamental solutions') for the Pucci?Heisenberg operators. Using these functions we obtain the continuity property, up to the boundary, for the viscosity solution of fully non-linear Dirichlet problems on the Heisenberg group, if the boundary of the domain satisfies some regularity geometrical assumptions (e.g., an exterior Heisenberg-ball condition at the characteristic points). We point out that the knowledge of the fundamental solutions allows us also to obtain qualitative properties of Hadamard, Liouville and Harnack type.