Fine singularity analysis of solutions to the Laplace equation: Berg's effect
Analysis of PDEs
2023-07-19 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1412.7005,
title = {Fine singularity analysis of solutions to the Laplace equation: Berg's effect},
author = {Adam Kubica and Piotr Rybka},
journal= {arXiv preprint arXiv:1412.7005},
year = {2023}
}