A two-phase free boundary problem for harmonic measure
[Un problème dans la frontière libre avec deux phases pour la mesure harmonique]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 4, pp. 859-905.

On étudie un problème dans la frontière libre avec deux phases, initialement examiné par Kenig et Toro [21], et on montre un résultat précis de régularité de Hölder. La difficulté essentielle est qu'il n'y a pas de conditions a priori de non-dégénérescence dans la condition de frontière libre. Par conséquent, nous devons déduire la non-dégénérescence en utilisant des formules de monotonie.

We study a 2-phase free boundary problem for harmonic measure first considered by Kenig and Toro [21] and prove a sharp Hölder regularity result. The central difficulty is that there is no a priori non-degeneracy in the free boundary condition. Thus we must establish non-degeneracy by means of monotonicity formulae.

DOI : 10.24033/asens.2297
Classification : 35R35, 42B37.
Keywords: Harmonic measure, free boundary problems, monotonicity formulas, two-phase problem.
Mot clés : Mesure harmonique, problèmes dans la frontière libre, formules de monotonie, problème avec deux phases. 
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     title = {A two-phase free boundary problem  for harmonic measure},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {859--905},
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     volume = {Ser. 4, 49},
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Engelstein, Max. A two-phase free boundary problem  for harmonic measure. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 4, pp. 859-905. doi : 10.24033/asens.2297. http://archive.numdam.org/articles/10.24033/asens.2297/

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