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.

Cutri', A., Tchou, N. (2007). Barrier functions for Pucci-Heisenberg operators and applications. INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS, 1(2), 117-131 [10.1504/IJDSDE.2007.016514].

Barrier functions for Pucci-Heisenberg operators and applications

CUTRI', ALESSANDRA;
2007-01-01

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.
2007
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
Heisenberg group, viscosity solutions, Pucci operators, Hamilton?Jacobi equations, barrier functions, nonlinear Dirichlet problems
Cutri', A., Tchou, N. (2007). Barrier functions for Pucci-Heisenberg operators and applications. INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS, 1(2), 117-131 [10.1504/IJDSDE.2007.016514].
Cutri', A; Tchou, N
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/34749
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