English

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}
}