About the Speaker
Guanying Peng
Speaker
Worcester Polytechnic Institute, U.S.
Speaker Sessions
- EST
Compactness and Regularity for a Generalized Aviles-Giga Functional
The classical Aviles-Giga functional is a well known second order energy functional that has been used to model smectic liquid crystals and thin film blisters. In this talk we will discuss a generalized Aviles-Giga functional in two dimensions, where the zero set of the potential is a strictly convex C1𝐶1 curve instead of S1𝑆1. Among other things, we generalize the notion of entropies, and use this tool to establish compactness for sequences with bounded energy and regularity for zero and finite energy states. Our analysis sheds light on what parts of the classical Aviles-Giga theory are contingent on specific algebraic properties of S1𝑆1, and what parts are more flexible. This is joint work with Xavier Lamy and Andrew Lorent.
