  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.
