Tangential limit values of a biharmonic poisson integral in a disk

Abstract

Let C ₀ be a curve in a disk D={|z|<1} that is tangent to the circle at the point z=1, and let C _θ be the result of rotation of this curve about the origin z=0 by an angle θ. We construct a bounded function biharmonic in D that has a zero normal derivative on the boundary and for which the limit along C _θ does not exist for all θ, 0≤θ≤2π.