ΕΚΔΗΛΩΣΕΙΣ

Ημερομηνία: 08/12/2022

Ώρα: 15:00

Τόπος: Αίθουσα Α32

Ομιλητης: Zhiyuan Geng, BCAM

Title: On the triple junction problem without symmetry hypotheses

Abstract: In this talk, I will present some joint work with Nicholas Alikakos on the vector Allen-Cahn equation with a triple-well potential.
Without assuming any symmetry hypothesis on the solution, we construct an entire minimizing solution that possesses a weak triple junction structure. A tight energy lower bound is established, which is crucial for estimates of the location and size of the diffuse interface. Other key tools used in our analysis include the 1D heteroclinic connection, Caffarelli-Córdoba density estimates and a blow-up analysis near the diffuse interface.