On a classical solvability of a Florin problem

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

On the solvability of the nonlinear problem for elliptic-parabolic system of the equations in Hölder spaces

There is proved the existence and the uniqueness of the solution of the nonlinear H.Amann problem for the parabolic-elliptic equations for the small time in the Holder spaces, the estimates for the solution are derived, the smoothness on t of the potential φ is obtained