Partial differential equations/Optimal control
Partial regularity for solutions to subelliptic eikonal equations
Comptes Rendus. Mathématique, Volume 356 (2018) no. 2, pp. 172-176.

On a bounded domain Ω in the Euclidean space Rn, 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 Rn. 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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.01.003
Albano, Paolo 1; Cannarsa, Piermarco 2; Scarinci, Teresa 3

1 Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40127 Bologna, Italy
2 Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy
3 University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
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Albano, Paolo; Cannarsa, Piermarco; Scarinci, Teresa. 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. http://www.numdam.org/articles/10.1016/j.crma.2018.01.003/

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