Singular limits for the two-phase Stefan problem

We prove strong convergence to singular limits for a linearized fully inhomogeneous Stefan problem subject to surface tension and kinetic undercooling effects. Different combinations of $\sigma \to {\sigma }_0$ and $\delta \to {\delta }_0$, where $\sigma ,{\sigma }_0\ge 0$ and $\delta ,{\delta }_0\ge 0$ denote surface tension and kinetic undercooling coefficients respectively, altogether lead to five different types of singular limits. Their strong convergence is based on uniform maximal regularity estimates.