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Abstract

We consider the multidimensional two-phase Stefan problem with a small parameter $\kappa$ in the Stefan condition, due to which the problem becomes singularly perturbed. We prove unique solvability and a coercive uniform (with respect to $\kappa$) estimate of the solution of the Stefan problem for $t\le T_0$, $T_0$ independent of $\kappa$, and the existence and estimate of the solution of the Florin problem (Stefan problem with $\kappa=0$) in Hölder spaces.