The two-phase problem for harmonic measure in VMO
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 Reifenber...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:288650 |
| Acceso en línea: | https://ddd.uab.cat/record/288650 https://dx.doi.org/urn:doi:10.1007/s00526-020-01760-2 |
| Access Level: | acceso abierto |
| Sumario: | 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. |
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