Mathematical Sciences Department
Analysis/PDE Seminar
Guanying Peng, WPI
Thursday, April 11, 2024
11:00 am – 12:00 pm
Unity Hall 400
Title: Rigidity of the Eikonal equation with $L^p$ entropies
Abstract: The Aviles-Giga functional is a classical problem in the calculus of variations. The energy functional in 2D was used to model smectic liquid crystals and thin film blisters. The Gamma-convergence of the Aviles-Giga functional remains a challenging open problem, which requires better understanding of the fine structure of the underlying function space, namely the space of \emph{finite entropy solutions} of the Eikonal equation. In this talk, I will give an introduction to the above mentioned problem, and present our recent progress towards understanding finite entropy solutions of the Eikonal equation in 2D. Our result supports the conjecture that entropy measures of finite entropy solutions concentrate on 1D sets, and completes the picture on the rigidity/flexibility threshold of the 2D Eikonal equation in the Besov space scaling. This is joint work with Xavier Lamy and Andrew Lorent.