Balayage of Measures : Behavior Near a Cusp
Let μ be a positive measure supported on a planar domain Ω. We consider the behavior of the balayage measure ν:=Bal(μ,∂Ω) near a point z0∈∂Ω at which Ω has an outward-pointing cusp. Assuming that the order and coefficient of tangency of the cusp are d>0 and a>0, respectively, and that dμ(z)≍|z-z0|2b-2d2z as z→z0 for some b>0 (here d2z is the Lebesgue measure on C), we obtain the leading order term
