Interface minimization of planar networks of branched interfaces

  • Sebastian Hensel (University of Bonn)
E1 05 (Leibniz-Saal)


The concept of paired calibrations due to Lawlor and Morgan (Pacific J.\ Math., 166, 1994) provides a particularly elegant tool for proving global area minimization of a network of branched interfaces as appearing in multiphase materials. In this talk, I will present a result on local interface area minimization for a class of stationary points of the interface energy which, due to Kinderlehrer and Liu (Math.\ Models Methods Appl.\ Sci., 11, 2001), occur as long-time asymptotic limits of multiphase mean curvature flow. This class contains continuous one-parameter families of stationary points which are not global minimizers. In particular, paired calibrations do not exist for those and consequently, minimality properties for such networks remained an open problem. Our result is based on a new concept of paired local calibrations allowing to overcome the difficulties associated with the above mentioned degeneracy of the energy landscape. This is joint work with Julian Fischer, Tim Laux and Theresa Simon (arXiv:2212.11840).

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
  • Mar 26, 2024 tba with Phan Thành Nam
  • Mar 26, 2024 tba with Dominik Schmid
  • May 7, 2024 tba with Manuel Gnann
  • May 14, 2024 tba with Barbara Verfürth
  • May 14, 2024 tba with Lisa Hartung
  • Jun 25, 2024 tba with Paul Dario
  • Jul 16, 2024 tba with Michael Loss