Title: Barrier functions for Pucci–Heisenberg operators and applications

Authors: Alessandra Cutri, Nicoletta Tchou

Addresses: Dipartimento di Matematica, Universita 'Tor Vergata' di Roma, 00133 Roma, Italy. ' IRMAR, Universite de Rennes 1, 35042 Rennes, France

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.

Keywords: Heisenberg group; viscosity solutions; Pucci operators; Hamilton–Jacobi equations; barrier functions; nonlinear Dirichlet problems.

DOI: 10.1504/IJDSDE.2007.016514

International Journal of Dynamical Systems and Differential Equations, 2007 Vol.1 No.2, pp.117 - 131

Published online: 06 Jan 2008 *

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