On boundary detachment phenomena for the total variation flow with dynamic boundary conditions
Yoshikazu Giga, Ryota Nakayashiki, Piotr Rybka, Ken Shirakawa · Journal of Differential Equations · 2020
We combine the total variation flow suitable for crystal modeling and image analysis with the dynamic boundary conditions. We analyze the behavior of facets at the parts of the boundary where these conditions are imposed. We devote particular attention to the radially symmetric data. We observe that the boundary layer detachment actually can happen at concave parts of the boundary.