A degenerate incompatible two-well problem related to quadrature domains and Hele-Shaw flowsOberseminar Analysis

by Mr Noah Piemontese-Fischer (University of Bonn)

Thursday Oct 22, 2026, 2:15 PM → 4:15 PM Europe/Berlin

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

In this talk, we study an incompatible two-well problem that exhibits some surprising flexibility properties. We consider two variants of the problem: one without gauge invariance and one with SO(2) invariance. Upon taking a glimpse at the relaxations of the energies, we discuss a connection between these variational problems and the theory of quadrature domains. This link allows us to construct minimizers with finite surface energy via tools from potential theory and free-boundary problems, including partial balayage, mother bodies and a squeezing-type Hele-Shaw flow. The talk is based on ongoing joint work with Lennart Machill and Angkana Rüland.