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In a previous work, we prove the existence of weak solutions to aninitial-boundary value problem, with $H^1(\Omega)$ initial data, for a systemof partial differential equations, which consists of the equations of linearelasticity and a nonlinear, degenerate parabolic equation of second order.Assuming in this article the initial data is in $H^2(\Omega)$, we investigatethe regularity of weak solutions that is difficult due to the gradient termwhich plays a role of a weight. The problem models the behavior in time ofmaterials with martensitic phase transitions. This model with diffusive phaseinterfaces was derived from a model with sharp interfaces, whose evolution isdriven by configurational forces, and can be thought to be a regularization ofthat model. Our proof, in which the difficulties are caused by the weight inthe principle term, is only valid in one space dimension.

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