Citation: |
[1] |
B. Bazaliy and S. P. Degtyarev, The classical Stefan problem as the limit case of the Stefan problem with a kinetic condition at the free boundary, Free Boundary Problems in Continuum Mechanics (Novosibirsk, 1991), Internat. Ser. Numer. Math., 106, Birkhäuser, Basel, (1992), 83-90. |
[2] |
R. Denk, M. Hieber and J. Prüss, "$\mathcal R$-Boundedness, Fourier Multipliers, and Problems of Elliptic and Parabolic Type," AMS Memoirs 788, Providence, R.I., 2003. |
[3] |
R. Denk, J. Prüss and R. Zacher, Maximal $L_p$-regularity of parabolic problems with boundary conditions of relaxation type, J. Funct. Anal., 255 (2008), 3149-3187.doi: 10.1016/j.jfa.2008.07.012. |
[4] |
R. Denk, J. Saal and J. Seiler, Inhomogeneous symbols, the Newton polygon, and maximal $L^p$-regularity, Russian J. Math. Phys. (2), 15 (2008), 171-192.doi: 10.1134/S1061920808020040. |
[5] |
J. Escher, J. Prüss and G. Simonett, Analytic solutions for a Stefan problem with Gibbs-Thomson correction, J. Reine Angew. Math., 563 (2003), 1-52.doi: 10.1515/crll.2003.082. |
[6] |
M. Hieber and J. Prüss, Functional calculi for linear operators in vector-valued $L^p$-spaces via the transference principle, Adv. Differential Equations, 3 (1998), 847-872. |
[7] |
N. Kalton and L. Weis, The $H^\infty$-calculus and sums of closed operators, Math. Ann., 321 (2001), 319-345.doi: 10.1007/s002080100231. |
[8] |
P. C. Kunstmann and L. Weis, Maximal $L_p$-regularity for parabolic equations, Fourier multiplier theorems and $H^\infty$-functional calculus, Functional analytic methods for evolution equations, Lecture Notes in Math., 1855, Springer, Berlin, (2004), 65-311.doi: 10.1007/978-3-540-44653-8_2. |
[9] |
M. Meyries and R. Schnaubelt, Interpolation, embeddings and traces of anisotropic fractional Sobolev spaces with temporal weights, J. Funct. Anal., 262 (2012), 1200-1229.doi: 10.1016/j.jfa.2011.11.001. |
[10] |
J. Prüss, J. Saal and G. Simonett, Existence of analytic solutions for the classical Stefan problem, Math. Ann., 338 (2007), 703-755.doi: 10.1007/s00208-007-0094-2. |
[11] |
J. Prüss and G. Simonett, Stability of equilibria for the Stefan problem with surface tension, SIAM J. Math. Anal., 40 (2008), 675-698.doi: 10.1137/070700632. |
[12] |
J. Prüss, G. Simonett and M. Wilke, On thermodynamically consistent Stefan problems with variable surface energy, submitted, arXiv:1109.4542. |
[13] |
J. Prüss, G. Simonett and R. Zacher, Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension, Arch. Ration. Mech. Anal., 207 (2013), 611-667.doi: 10.1007/s00205-012-0571-y. |
[14] |
H. Triebel, "Interpolation Theory, Function Spaces, Differential Operators," North-Holland, Amsterdam, 1978. |
[15] |
H. Triebel, "Theory of Function Spaces," 78 of Monographs in Mathematics, Birkhäuser, Basel, 1983.doi: 10.1007/978-3-0346-0416-1. |
[16] |
T. Youshan, The limit of the Stefan problem with surface tension and kinetic undercooling on the free boundary, J. Partial Differential Equations, 9 (1996), 153-168. |