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Multi-phase minimizers for the Allen-Cahn system on the plane

3 May@14h00-15h00

Séminaire du LJLL

Nicholas Alikakos (Université d’Athènes)

In this talk we investigate multi-phase minimizers for the Allen-Cahn system on the plane. Our emphasis is on distinct surface tension coefficients. The proofs do not rely on symmetry.
Coexistence of an arbitrary number of phases is related to the existence of the relevant minimizing cones for the minimal partition problem. For example, the orthogonal cross with four phases is minimizing for a certain class of surface tension coefficients. We focus on two examples: the entire solution for the triple junction, and a four-phase minimizer with three-phase Dirichlet data (the triangle).
The results presented in the talk are based on joint work with Zhiyuan Geng (the triple junction), and with Dimitrios Gazoulis (the triangle).

Diaporama du séminaire de Nicholas Alikakos 03 mai 2024 – 1 Mo


3 May
Event Category:


Séminaire du LJLL - Nicholas Alikakos (Université d'Athènes)