Colloquium

Separating Microstructure

by Kewei Zhang, Professor of Mathematics, University of Sussex, UK

Abstract

We begin with a brief survey on how to use partialdifferential equation techniques to study oscillation of weakconvergent sequences of gradients approaching a compact set whichmodels materials microstructure. Some results on separation ofmicrostructure (gradient Young measures) are discussed. A sketchof the proof for the case of neighborhoods of a two-point set isgiven. The proof involves applications of the BMO-estimates forlinear elliptic systems and homogeneous Young measures.