Partial Differential Equations
Fully nonlinear degenerate operators associated with the Heisenberg group: barrier functions and qualitative properties
Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 559-563.

The aim of this Note is to state some continuity property, up to the boundary, for viscosity solutions to fully nonlinear Dirichlet problems on the Heisenberg group and to obtain qualitative properties of the Hadamard, Liouville and Harnack type. For this purpose, a key ingredient is the construction of some barrier functions for the Pucci–Heisenberg operators.

Nous déterminons des propriétés de continuité jusqu'au bord des solutions de viscosité pour le problème de Dirichlet pour des opérateurs completement non-linéaires associés au groupe de Heisenberg. Pour ces opérateurs nous provons aussi des propriétés de Hadamard, Liouville et Harnack. L'outil essentiel est la constructions de fonctions barrière pour les opérateurs de Pucci–Heisenberg.

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DOI: 10.1016/j.crma.2007.03.003
Cutrì, Alessandra 1; Tchou, Nicoletta 2

1 Dipartimento di Matematica, Università di Roma, “Tor Vergata” 00133 Roma, Italy
2 IRMAR, Université de Rennes 1, campus de Beaulieu, 35042 Rennes cedex, France
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Cutrì, Alessandra; Tchou, Nicoletta. Fully nonlinear degenerate operators associated with the Heisenberg group: barrier functions and qualitative properties. Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 559-563. doi : 10.1016/j.crma.2007.03.003. http://www.numdam.org/articles/10.1016/j.crma.2007.03.003/

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