Applied Analysis Seminar Convergence of thresholding energies for anisotropic mean curvature flow on inhomogeneous obstacle

In this talk, I will present a recent joint work with Karel Švadlenka (Tokyo Metropolitan University). We extend the analysis by Esedoglu and Otto (2015) of thresholding energies for the celebrated multiphase Bence-Merriman-Osher algorithm for computing mean curvature flow of interfacial networks to the case of differing space-dependent anisotropies. In particular, we address the special setting of an obstacle problem, where anisotropic particles move on an inhomogeneous substrate. By suitable modification of the surface energies, we construct an approximation that uses a single convolution kernel and is monotone with respect to the convolution width, and we prove that the approximate energies \Gamma-converge to their sharp interface counterpart.