On a classical solvability of a Florin problem

Abstract

There is considered the multidimensional two-phase Stefan problem with a small parameter k at the velocity of a free boundary in a Stefan condition. The unique solvability and coercive uniform with respect to k estimate of the solution for t ≤ T₀, T₀ - independent on k, are proved and on the basis of this the existence, uniqueness and estimate of the solution of a Florin problem (Stefan problem with k = 0) are obtained in the Holder spaces.