报告题目：On the planar triple junction problem for the Allen-Cahn system

报告人： 耿志远 教授(Purdue University)

报告时间：2024年6月18日 上午 8:30 -9:30

报告地点： 数理楼135

报告摘要：For the scalar two-phase (elliptic) Allen-Cahn equation, there is a rich literature on the celebrated De Giorgi conjecture, which establishes the relationship between diffuse interfaces and minimal surfaces. Analogously, the coexistence of three or more phases is related to the minimizing cones for the minimal partition problem. In this talk, we investigate the vector-valued Allen-Cahn equation with a potential vanishing at three energy wells. We establish the existence of a minimizing entire solution that converges to a unique triple junction at infinity. The location and size of the diffuse interface are estimated from tight energy upper and lower bounds. Our proof does not rely on any symmetry hypotheses on the solution or the potential. The results presented in this talk are based on joint work with Nicholas Alikakos.

报告人简介： 耿志远，2020年在纽约大学柯朗研究所获得博士学位，目前为美国普渡大学访问助理教授。主要研究方向为偏微分方程，变分学，几何测度论，以及在液晶模型，相变模型，自由边界问题中的应用。已在ARMA, JFA, CVPDE. 等国际高水平期刊发表论文多篇。