Fine singularity analysis of solutions to the Laplace equation: Berg's   effect
  We study Berg's effect on special domains. This effect is understood as monotonicity of a harmonic function (with respect to the distance from the center of a flat part of the boundary) restricted to the boundary. The harmonic function must satisfy piecewise constant Neumann boundary conditions. We show that Berg's effect is a rare and fragile phenomenon. 
Adam Kubica, Piotr Rybka
math.AP