Phase transitions with Allen-Cahn mean curvature bounded in Lp

Abstract

摘要

We consider the varifolds associated to a phase transition problem whose first variation of Allen-Cahn energy is Lp integrable with respect to the energy measure. We can see that the Dirichlet and potential part of the energy are almost equidistributed. After passing to the phase field limit, one can obtain an integer rectifiable varifold with bounded Lp mean curvature. This is joint work with Huy Nguyen.

About the speaker

主讲人介绍

I am currently a lecturer in the school of mathematical sciences in Queen Mary University of London.

I do research in geometric analysis and partial differential equations. More specifically, I am interested in the regularity theory and singularity analysis of geometric partial differential equations (e.g. minimal surfaces, mean curvature flows, Ricci flows and the Allen-Cahn equations) and their applications in geometric topology and mathematical relativity.

I obtained my PhD from Johns Hopkins University in 2018. Before joining QMUL as a lecturer, I have held postdoc positions in SUNY Binghamton, QMUL and Warwick.