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Continuous differentiability of the free boundary for weak solutions of the Stefan problem. (English) Zbl 0278.35054


MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35D10 Regularity of generalized solutions of PDE (MSC2000)
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References:

[1] J. R. Cannon and C. Denson Hill, Existence, uniqueness, stability, and monotone dependence in a Stefan problem for the heat equation, J. Math. Mech. 17 (1967), 1 – 19. · Zbl 0154.36403
[2] J. R. Cannon, Jim Douglas Jr., and C. Denson Hill, A multi-boundary Stefan problem and the disappearance of phases, J. Math. Mech. 17 (1967), 21 – 33. · Zbl 0154.36501
[3] John R. Cannon and Mario Primicerio, A two phase Stefan problem with temperature boundary conditions, Ann. Mat. Pura Appl. (4) 88 (1971), 177 – 191 (English, with Italian summary). · Zbl 0219.35046 · doi:10.1007/BF02415066
[4] Avner Friedman, The Stefan problem in several space variables, Trans. Amer. Math. Soc. 133 (1968), 51 – 87. · Zbl 0162.41903
[5] Avner Friedman, One dimensional Stefan problems with nonmonotone free boundary, Trans. Amer. Math. Soc. 133 (1968), 89 – 114. · Zbl 0162.42001
[6] S. L. Kamenomostskaja, On Stefan’s problem, Mat. Sb. (N.S.) 53 (95) (1961), 489 – 514 (Russian).
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