TY - JOUR
T1 - On a two-phase problem for harmonic measure in general domains
AU - Azzam, Jonas
AU - Mourgoglou, Mihalis
AU - Tolsa, Xavier
AU - Volberg, Alexander
PY - 2019/10/1
Y1 - 2019/10/1
N2 - © 2019 by Johns Hopkins University Press. We show that, for disjoint domains in the Euclidean space, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries. This improves on our previous result which assumed that the boundaries satisfied the capacity density condition.
AB - © 2019 by Johns Hopkins University Press. We show that, for disjoint domains in the Euclidean space, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries. This improves on our previous result which assumed that the boundaries satisfied the capacity density condition.
U2 - 10.1353/ajm.2019.0032
DO - 10.1353/ajm.2019.0032
M3 - Article
VL - 141
SP - 1259
EP - 1279
JO - American Journal of Mathematics
JF - American Journal of Mathematics
SN - 0002-9327
ER -