Speaker
Zhiyuan Geng
(PURDUE)
Description
(Zhiyuan Geng - Purdue University)
In this talk, we will discuss recent results on the 2D Allen-Cahn system with a triple-well potential. By studying the blow-up limit of solutions near the junction of three phases, we construct an entire minimizing solution that asymptotically converges at infinity to a unique triple junction, corresponding to a planar minimal cone. We further establish the almost 1D symmetry of the solution along the sharp interface. A key estimate in our analysis is the sharp energy lower and upper bounds, which enable the localization of the diffuse interface within a small neighborhood of the limiting interface. The results don't rely on any symmetry assumptions.
This is joint work with Nicholas Alikakos.
