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Barrier functions for Pucci-Heisenberg operators and applications

Alessandra Cutri·Nicoletta Tchou
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Abstract

The aim of this article 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 also to obtain qualitative properties of Hadamard, Liouville and Harnack type.

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Alessandra Cutri, Nicoletta Tchou. 2007-02-27. Barrier functions for Pucci-Heisenberg operators and applications. https://arxiv.org/abs/math/0702818

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