Local regularity of solutions of variational problems for the equilibrium configuration of an incompressible, multiphase elastic body (Q5937991)

The authors consider a multiphase, incompressible, elastic body with \(k\) preferred states whose equilibrium configuration is described in terms of a nonconvex variational problem. After passing to a suitable relaxed variational integral whose solution has the meaning of the strain tensor, the associated dual problem for the stresses is also studied. It is shown smoothness of the strain tensor near any point of strict \(J^1_m\)-quasiconvexity of the relaxed integrand. This result is used in order to get regularity of the stress tensor on the union of pure phases at least in the two-dimensional case.