Interpolation Inequalities and Pattern Formation in Variational Models for MembranesOberseminar Analysis

by Dr Anastasija Pesic (Weierstrass Institute Berlin)

Thursday Apr 23, 2026, 2:00 PM → 4:00 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

In this talk, we will discuss pattern formation in variational models for biological membranes, motivated by lipid raft formation. As a starting point, we consider an approximation of a two-phase Canham-Helfrich functional and present a scaling law for the minimal energy.
A central ingredient in the lower bound is a class of new nonlocal and nonlinear interpolation inequalities, which control fractional Sobolev seminorms in terms of Modica-Mortola-type energies.
Motivated by the scaling law, we then study a related functional with competing local and nonlocal terms and indicate results and open questions concerning the structure of minimizers.
The talk is based on joint work with Barbara Zwicknagl and Janusz Ginster, and on ongoing work with Sara Daneri and Eris Runa.