Classical solvability of multidimensional two-phase Stefan problem for degenerate parabolic equations and Schauder’s estimates for a degenerate parabolic problem with dynamic boundary conditions

  • S. P. DegtyarevEmail author


We consider multidimensional two-phase Stefan problem for degenerate parabolic equations of the porous medium type in classes of smooth functions. First we find a natural Hölder class for the Dirichlet boundary conditions in the initial boundary boundary problem for a degenerate parabolic equation of second order. This class then is used to obtain the Schauder estimates for a degenerate parabolic equation with dynamic boundary conditions. As a result we prove the existence locally in time of a smooth solution for Stefan problem for degenerate parabolic equations.

Mathematics Subject Classification (2010)

Primary 35R35 Secondary 35K65 35R37 35K60 


Free boundary Stefan problem Classical solvability Porous medium equation Degenerate parabolic equations Dynamic boundary conditions Schauder estimates 


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Authors and Affiliations

  1. 1.Institute of Applied Mathematics and Mechanics NASUDonetskUkraine

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