Partial regularity for solutions to subelliptic eikonal equations

Albano, Paolo; Cannarsa, Piermarco; Scarinci, Teresa

doi:10.1016/j.crma.2018.01.003

Partial differential equations/Optimal control

Partial regularity for solutions to subelliptic eikonal equations
[Sur la régularité partielle des solutions de l'équation eikonale sous-elliptique]

Présenté par : Jean-Michel Coron

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

Comptes Rendus. Mathématique, Tome 356 (2018) no. 2, pp. 172-176.

Résumé
Abstract

Soit Ω un ouvert borné à bord lisse de $R^{n}$ . 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.

On a bounded domain Ω in the Euclidean space $R^{n}$ , 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.

Reçu le : 2017-08-07
Accepté le : 2018-01-08
Publié le : 2018-02-01

DOI : 10.1016/j.crma.2018.01.003

Affiliations des auteurs :

Albano, Paolo ¹ ; Cannarsa, Piermarco ² ; Scarinci, Teresa ³

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     author = {Albano, Paolo and Cannarsa, Piermarco and Scarinci, Teresa},
     title = {Partial regularity for solutions to subelliptic eikonal equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {172--176},
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     volume = {356},
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     doi = {10.1016/j.crma.2018.01.003},
     language = {en},
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Albano, Paolo; Cannarsa, Piermarco; Scarinci, Teresa. Partial regularity for solutions to subelliptic eikonal equations. Comptes Rendus. Mathématique, Tome 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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