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math.AP2014★ 5 cited
Fine singularity analysis of solutions to the Laplace equation: Berg's effect
Adam Kubica, Piotr Rybka
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 boun…
math.AP2014
Oscillating facets
Milena Matusik, Piotr Rybka
We study a singular one-dimensional parabolic problem with initial data in the space, the energy space, for various boundary data. We pay special attention to Dirichlet condit…