PDEA Seminar: Minimal surfaces and Allen-Cahn equations

Abstract: Minimal surfaces and Allen--Cahn equations are central topics in geometric partial differential equations and geometric measure theory. We provide a brief overview of the research history, with particular focus on the interface regularity of Allen--Cahn equations. We then introduce a promising new approach to second-order interface regularity for Allen--Cahn-type equations, based on the new discrepancy–curvature equation. Since the above equation holds for any semilinear equation, we expect that this approach is flexible and has broader applications beyond Allen--Cahn equations.

This is a seminar in the PDEs and Applications seminar series.