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| Pàgina inicial > Articles > Articles publicats > The two-phase problem for harmonic measure in VMO |
(Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universitat Autònoma de Barcelona. Departament de Matemàtiques)| Data: | 2020 |
| Resum: | Let Ω +⊂ Rn+1 be an NTA domain and let Ω -= Rn+1\ Ω +¯ be an NTA domain as well. Denote by ω+ and ω- their respective harmonic measures. Assume that Ω + is a δ-Reifenberg flat domain for some δ> 0 small enough. In this paper we show that logdω-dω+∈VMO(ω+) if and only if Ω + is vanishing Reifenberg flat, Ω + and Ω - have joint big pieces of chord-arc subdomains, and the inner unit normal of Ω + has vanishing oscillation with respect to the approximate normal. This result can be considered as a two-phase counterpart of a more well known related one-phase problem for harmonic measure solved by Kenig and Toro. |
| Ajuts: | Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-0395 Ministerio de Ciencia e Innovación MTM-2016-77635-P Ministerio de Economía y Competitividad MTM-2016-77635-P Ministerio de Economía y Competitividad MDM-2014-044 European Commission 834728 |
| Drets: | Tots els drets reservats.  |
| Llengua: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Publicat a: | Calculus of Variations and Partial Differential Equations, Vol. 59, Issue 3 (June 2020) , art. 102, ISSN 1432-0835 |
