On scaling properties for two-state problems

Camillo Tissot (Heidelberg University) #

We study quantitative rigidity properties for the compatible and incompatible two-state problems for suitable classes of A-free operators. In particular, in the compatible setting we prove that all homogeneous, first order, linear operators with affine boundary data which enforce oscillations yield the typical epsilon-2/3-lower scaling bounds. As observed by Chan and Conti [CC15] for higher order operators this may no longer be the case. Revisiting the example from Chan and Conti, we show that this is reflected in the structure of the associated symbols and that this can be exploited for a new Fourier based proof of the lower scaling bound.