Fine singularity analysis of solutions to the Laplace equation, Berg effect

Adam Kubica , Piotr Rybka


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.
Author Adam Kubica ZRF
Adam Kubica,,
- Department of Functional Equations
, Piotr Rybka
Piotr Rybka,,
Journal seriesMathematical Methods in the Applied Sciences, ISSN 0170-4214
Issue year2016
Publication size in sheets0.5
Keywords in Englishsingularities of harmonic functions, polygonal domains, piecewise constant Neumann data, Berg’s effect
Abstract in PolishW pracy badano zachodzenie tzw. efektu Berga w specjalnych obszarach wielokątnych. Korzystając z wcześniejszych rezultatów pokazano, iż efekt ten jest niestabilny. Mianowicie, zaburzenie obszaru w którym efekt Berga zachodzi prowadzi do jego zaniku.
Languageen angielski
Score (nominal)25
ScoreMinisterial score = 25.0, 28-11-2017, ArticleFromJournal
Ministerial score (2013-2016) = 25.0, 28-11-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 1.017 (2) - 2016=1.031 (5)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.