Various Mathematical Questions Arising in Phase Separation Problem

  • Yoshihiro Tonegawa (Hokkaido University)
A3 01 (Sophus-Lie room)


The Modica-Mortola functional of phase transitions is well-known to Gamma converge to the hypersurface area functional as the small parameter tends to zero. It is now known that the control of mean curvature-like quantity is sufficient for the convergence, and more subtle questions can be asked about its property. I review some known results along with open problems and discuss related problems such as Allen-Cahn equation with or without coupled terms, Cahn-Hilliard equation and a functional motivated by the large deviation theory. Some of the questions are of technical and others of intrinsic geometric nature in the setting of geometric measure theory.

Anne Dornfeld

MPI for Mathematics in the Sciences Contact via Mail

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