Bounds for effective strains of geometrically linear elastic multiwell model

We give a direct estimate for the quasiconvex hull Qe(K) on linear strains generated by a finite set of linear strains of symmetric matrices. The problem is directly related to the microstructure modelled by the multiwell problem and its corresponding macroscopic effect. We bound the quasiconvex envelope Qedist(e(X),K) near an exposed edge of the convex hull C(K) that does not have compatible connections. Our bounds depend on the weak type-(1,1) estimate for certain singular integral operators and the geometric properties of the exposed edge.