2026-04-17T20:42:30Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/5307322024-12-20T04:58:00Zcom_2072_199267com_2072_4427col_2072_201036

The two-phase problem for harmonic measure in VMO Prats, M. Tolsa, X. Matemàtiques 51 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. 2020-05-20 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://hdl.handle.net/2072/530732 10.1007/s00526-020-01760-2 eng Calculus of Variations and Partial Differential Equations L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons:http://creativecommons.org/licenses/by-nc-sa/4.0/ info:eu-repo/semantics/openAccess 59 p. application/pdf Springer RECERCAT (Dipòsit de la Recerca de Catalunya)