Regularity of solutions to a model for solid-solid phase transitions driven by configurational forces

In a previous work, we prove the existence of weak solutions to an initial-boundary value problem, with H1(Ω) initial data, for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear, degenerate parabolic equation of second order. This problem models the behavior in time of materials with martensitic phase transitions. This model with diffusive phase interfaces was derived from a model with sharp interfaces, whose evolution is driven by configurational forces, and can be regarded as a regularization of that model. Assuming in this article the initial data is in H2(Ω), we investigate the regularity of weak solutions that is difficult due to the gradient term which plays a role of a weight. Our proof, in which the difficulties are caused by the weight in the principle term, is only valid in one space dimension.