caa a22 4500 606194495 CHVBK 20210128100914.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00030-014-0280-3 doi (NATIONALLICENCE)springer-10.1007/s00030-014-0280-3 Degtyarev S. Institute of Applied Mathematics and Mechanics NASU, R.Luxemburg str. 74, 83114, Donetsk, Ukraine aut 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 [Elektronische Daten] [S. Degtyarev] 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. Springer Basel, 2014 Free boundary nationallicence Stefan problem nationallicence Classical solvability nationallicence Porous medium equation nationallicence Degenerate parabolic equations nationallicence Dynamic boundary conditions nationallicence Schauder estimates nationallicence Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/2(2015-04-01), 185-237 1021-9722 22:2<185 2015 22 30 https://doi.org/10.1007/s00030-014-0280-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-014-0280-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Degtyarev S. Institute of Applied Mathematics and Mechanics NASU, R.Luxemburg str. 74, 83114, Donetsk, Ukraine aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/2(2015-04-01), 185-237 1021-9722 22:2<185 2015 22 30