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math.AP2013
Fine singularity analysis of solutions to Laplace equation
Adam Kubica, Piotr Rybka
We present here a fine singularity analysis of solutions to the Laplace equation in special polygonal domains in the plane. We assume piecewise constant Neumann on one component of…
math.AP2013★ 3 cited
Two cases of squares evolving by anisotropic diffusion
Piotr B. Mucha, Monika Muszkieta, Piotr Rybka
We are interested in an anisotropic singular diffusion equation in the plane and in its regularization. We establish existence, uniqueness and basic regularity of solutions to both…