The two-phase problem for harmonic measure in VMO
Let Ω+⊂ℝ+1 be an NTA domain and let Ω−=ℝ+1∖Ω+⎯⎯ be an NTA domain as well. Denote by + and − their respective harmonic measures. Assume that Ω+ is a -Reifenberg flat domain for some >0 small enough. In this paper we show that log−+∈VMO(+) if and only if Ω+ is vanishing Reifenberg flat, Ω+ and Ω− h...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/530732 |
| Acesso em linha: | http://hdl.handle.net/2072/530732 |
| Access Level: | acceso abierto |
| Palavra-chave: | Matemàtiques 51 |
| Resumo: | Let Ω+⊂ℝ+1 be an NTA domain and let Ω−=ℝ+1∖Ω+⎯⎯ be an NTA domain as well. Denote by + and − their respective harmonic measures. Assume that Ω+ is a -Reifenberg flat domain for some >0 small enough. In this paper we show that log−+∈VMO(+) 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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