Relaxation of three solenoidal wells and characterization of three phase H-measures

We study the problem of characterizing quasiconvex hulls for three solenoidal (divergence free) wells in dimension three when the wells are pairwise incompatible. We provide the characterization for a generic regime by translating the problem into the language of H-measures. As a by-product we obtain the characterization of a class of three-point H-measures associated with three phase mixtures of characteristic functions in dimension three.

(This is a joint work with V. P. Smyshlyaev).