"Rigidity Estimate for Two Incompatible Wells and its Application"
It is well know that the special orthogonal group SO(n) does not support the fine scale oscillation of the gradients. Recently Friesecke, James and Mueller established a quantitative version of this phenomena. However it is not known whether two incompatible (without rank-one connections) copies of SO(n) support microstructures. We will discuss an optimal quantitative rigidity estimate for two `strongly incompatible' (in the sense of Matos and Sverak) copies of SO(n). We will also discuss an application to the scaling of thin martensitic films. This is a joint work with Stefan Mueller.
THURSDAY, December 6, 2005