On a Sharp Interface Limit of the Kobayashi-Warren-Carter Energy

This lecture explores the sharp interface limit of the Kobayashi-Warren-Carter energy system, which models grain structure evolution. Discover the characterization of this singular limit and examine its gradient flow under appropriate scaling, which yields a gradient flow involving fractional time derivatives. Learn about the properties of minimizers with fidelity terms plus total variation type energy, particularly in one-dimensional settings where all minimizers must be piecewise constant. The presentation draws from collaborative research with A. Kubo, H. Kuroda, J. Okamoto, K. Sakakibara, and M. Uesaka, and was delivered as part of the "Degenerate and Singular PDEs" workshop at the Erwin Schrödinger International Institute for Mathematics and Physics.