On a bounded domain Ω in the Euclidean space , we study the homogeneous Dirichlet problem for the eikonal equation associated with a system of smooth vector fields, which satisfies Hörmander's bracket generating condition. We prove that the solution is smooth in the complement of a closed set of Lebesgue measure zero.
Soit Ω un ouvert borné à bord lisse de . Nous étudions le problème de Dirichlet homogène sur Ω pour l'équation eikonale associée à un système de champs de vecteurs qui satisfait la condition de Hörmander. Nous montrons que la solution de ce problème est régulière dans le complémentaire d'un ensemble fermé de mesure de Lebesgue nulle.
Accepted:
Published online:
Paolo Albano 1; Piermarco Cannarsa 2; Teresa Scarinci 3
@article{CRMATH_2018__356_2_172_0,
author = {Paolo Albano and Piermarco Cannarsa and Teresa Scarinci},
title = {Partial regularity for solutions to subelliptic eikonal equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {172--176},
publisher = {Elsevier},
volume = {356},
number = {2},
year = {2018},
doi = {10.1016/j.crma.2018.01.003},
language = {en},
}
TY - JOUR AU - Paolo Albano AU - Piermarco Cannarsa AU - Teresa Scarinci TI - Partial regularity for solutions to subelliptic eikonal equations JO - Comptes Rendus. Mathématique PY - 2018 SP - 172 EP - 176 VL - 356 IS - 2 PB - Elsevier DO - 10.1016/j.crma.2018.01.003 LA - en ID - CRMATH_2018__356_2_172_0 ER -
Paolo Albano; Piermarco Cannarsa; Teresa Scarinci. Partial regularity for solutions to subelliptic eikonal equations. Comptes Rendus. Mathématique, Volume 356 (2018) no. 2, pp. 172-176. doi : 10.1016/j.crma.2018.01.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.01.003/
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