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1 DIPMAT - Dipartimento di Matematica Roma II 2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Keywords : Heisenberg group Viscosity solutions Regularity of solutions of Dirichlet problems Pucci operators Hadamard Liouville and Harnack type-properties

Author: Alessandra Cutri - Nicoletta Tchou -



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