Sets of absolute continuity for harmonic measure in NTA domains

2014/10/10 by Azzam, Jonas
#28A75 #28A78 #31A15 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1410.2782

Abstract

We show that if Ω is an NTA domain with harmonic measure w and E⊆ ∂Ω is contained in an Ahlfors regular set, then w|_E≪ \mathscrH^d|_E. Moreover, this holds quantitatively in the sense that for all τ>0 w obeys an A_∞-type condition with respect to \mathscrH^d|_E', where E'⊆ E is so that w(E\backslash E')

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