Regularity of the free boundary for non degenerate phase transition problems of parabolic type
Rendiconti del Seminario Matematico della Università di Padova, Tome 104 (2000), pp. 27-42.
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     author = {Fornari, L.},
     title = {Regularity of the free boundary for non degenerate phase transition problems of parabolic type},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {27--42},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {104},
     year = {2000},
     zbl = {1017.35119},
     mrnumber = {1809347},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2000__104__27_0/}
}
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Fornari, L. Regularity of the free boundary for non degenerate phase transition problems of parabolic type. Rendiconti del Seminario Matematico della Università di Padova, Tome 104 (2000), pp. 27-42. http://www.numdam.org/item/RSMUP_2000__104__27_0/

[1] 1 Athanasopoulos - L. A. CAFFARELLI - S. SALSA, Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems, Annals of Math., 143 (1996), pp. 413-434. | MR 1394964 | Zbl 0853.35049

[2] I. Athanasopoulos - L. A. CAFFARELLI - S. SALSA, Regularity of the free boundary in parabolic phase transition problems, Acta Math., 176 (1996), pp. 245-282. | MR 1397563 | Zbl 0891.35164

[3] L.A. Caffarelli, A Harnack inequality approach to the regularity of free [3] boundaries, Part I, Lipschitz free boundaries are C1,a, Rev. Math. Iberoamericana, 3 (1987), pp. 139-162. | MR 990856 | Zbl 0676.35085

[4] L.A. Caffarelli, A Harnack inequality approach to the regularity offree boundaries, Part II, Flat free boundaries are Lipschitz, Comm. Pure Appl. Math., 42 (1989), pp. 55-78. | MR 973745 | Zbl 0676.35086

[5] L.A. Caffarelli - L. C. EVANS, Continuity of the temperature in the two phase Stefan problems, Arch. Rat. Mech. Anal., 81 (3) (1983), pp. 199-220. | MR 683353 | Zbl 0516.35080

[6] L.A. Caffarelli - N. Wolanski, C1,α regularity of the free boundary for the N-dimensional porus media equation, Comm. Pure Appl. Math., 43 (1990), pp. 885-902. | Zbl 0728.76103

[7] E.B. Fabes - N. Garofalo - S. Salsa, A backward Harnack inequality and Fatou Theorem for nonnegative solutions of parabolic equations, Ill. Journal of Math., 30 (4) (1986), pp. 536-565. | MR 857210 | Zbl 0625.35006

[8] E.B. Fabes - N. Garofalo - S. Salsa, Comparison Theorems for temperatures in non-cylindrical domains, Atti Accad. Naz. Lincei, Ser. 8 Rend., 78 (1984), pp. 1-12. | MR 884371 | Zbl 0625.35007

[9] L. Fornari, Regularity of the solution and of the free boundary for free boundary problems arising in combustion theory, Ann. di Matem. pura ed appl., (IV) 176 (1999), pp. 273-286. | MR 1746545 | Zbl 0952.35156

[10] A. Friedman, The Stefan problem in several space variables, Trans. Amer. Math. Soc., 133 (1968), pp. 51-87. | MR 227625 | Zbl 0162.41903

[11] C. Lederman - N. WOLANSKI, Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem, Ann. Scuola Norm. Sup. Pisa Cl. Sci. Journal of Math. (4), 27 (1998), pp. 253-288. | Numdam | MR 1664689 | Zbl 0931.35200

[12] A.M. Meirmanov, On the classical solution of the multidimensional Stefan problem for quasilinear parabolic equations, Math. U.S.S.R.-Sbornik, 40 (1981), pp. 157-178. | Zbl 0467.35053

[13] R.H. Nochetto, A class of non-degenerate two-phase Stefan problem in several space variables, Comm. P.D.E., 12 (1) (1987), pp. 21-45. | MR 869101 | Zbl 0624.35085

[14] L. Rubenstein, The Stefan problem: comments on its present state, J. Inst. Maths. Applics., 124 (1979), pp. 259-277. | MR 550476 | Zbl 0434.35086

[15] D.A. Tarzia, A bibliography on moving-free boundary problems for the heat equation. The Stefan problem, Prog. Naz. M.P.I. Ital., Firenze 1988. | MR 1007840

[16] A. Visintin, Models of phase transitions, Birkhäuser, Boston 1996. | MR 1423808 | Zbl 0882.35004

[17] K.O. Widman, Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations, Math. Scand., 21 (1967), pp. 17-37. | MR 239264 | Zbl 0164.13101