Fine singularity analysis of solutions to the Laplace equation: Berg's effect.

J. Banasiak We study Berg's effect on special domains. This effect is understood as a 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. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]