[Opérateurs completement non-linéaires associés au groupe de Heisenberg : fonctions barrière et propriétés qualitatives]
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.
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.
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@article{CRMATH_2007__344_9_559_0,
author = {Alessandra Cutr{\`\i} and Nicoletta Tchou},
title = {Fully nonlinear degenerate operators associated with the {Heisenberg} group: barrier functions and qualitative properties},
journal = {Comptes Rendus. Math\'ematique},
pages = {559--563},
publisher = {Elsevier},
volume = {344},
number = {9},
year = {2007},
doi = {10.1016/j.crma.2007.03.003},
language = {en},
}
TY - JOUR AU - Alessandra Cutrì AU - Nicoletta Tchou TI - Fully nonlinear degenerate operators associated with the Heisenberg group: barrier functions and qualitative properties JO - Comptes Rendus. Mathématique PY - 2007 SP - 559 EP - 563 VL - 344 IS - 9 PB - Elsevier DO - 10.1016/j.crma.2007.03.003 LA - en ID - CRMATH_2007__344_9_559_0 ER -
%0 Journal Article %A Alessandra Cutrì %A Nicoletta Tchou %T Fully nonlinear degenerate operators associated with the Heisenberg group: barrier functions and qualitative properties %J Comptes Rendus. Mathématique %D 2007 %P 559-563 %V 344 %N 9 %I Elsevier %R 10.1016/j.crma.2007.03.003 %G en %F CRMATH_2007__344_9_559_0
Alessandra Cutrì; Nicoletta Tchou. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.003/
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