Properties of the phase boundary in the parabolic problem with hysteresis

We study solutions of parabolic equations with a discontinuous hysteresis operator, described by a free interface boundary. It is established that for spatially transverse initial data from the space $W_q^{2-2\mathrm{/}q}$ with $q>3$, there exists a solution in the space $W_q^{2,1}$, where the interface boundary exhibits Holder continuity with an exponent $1\mathrm{/}2$. Furthermore for initial data from the space $W_{\mathrm{\infty }}^2$, it is proven that the interface boundary satisfies the Lipschitz condition. It is shown that for non-transversal initial data, solutions with an interface boundary do not exist.