Uniqueness and existence results on the Hele-Shaw and the Stefan problems

Archive for Rational Mechanics and Analysis

Volumn 168, Issue 4, 2003, Pages 299-328

  Kim, Inwon C ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0043245213     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00205-003-0251-z     Document Type: Article

References (14)

1. [ACS] ATHANASOPOULOS, I., CAFFARELLI, L., SALSA, S.: Regularity of the free boundary in parabolic phase-transition problems. Acta Math. 176, 245-282 (1996)
2. [CC] CAFFARELLI, L., CABRE, X.: Fully nonlinear elliptic equations. AMS colloquium publications, Vol 43
3. [CIL] CRANDALL, M.G., ISHII, H., LIONS, P.L.: User's guide to viscosity solutions of second-order partial differential equations. Bull. Amer. Math. Sc. 27(1), 1-67 (1992)
4. [CL] CRANDALL, M.G., LIONS, P.L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277, 1-42 (1983)
5. [CV] CAFFARELLI, L., VAZQUEZ, J.L.: Viscosity solutions for the porous medium equation. Differential equations: La Pietra 1996 (Florence), 13-26, Proc. Sympos. Pure Math. 65, Amer. Math. Soc, Providence, RI (1999)
6. [D] DUVAUT, G.: Resolution d'un problème de Stefan. C. R. Acad. Sci. Paris Ser. A. 276, 1461-1463 (1973)
7. [EJ] ELLIOT, C.M., JANOVSKY, V.: A variational inequality approach to Hele-Shaw flow with a moving boundary. Proc. Roy. Soc. Edinburgh. Sect. A 88, 93-107 (1981)
8. [ES] ESCHER, J., SIMONETT, G.: Classical solutions of multidimensional Hele-Shaw models. SIAM J. Math. Anal 28, 1028-1047 (1997)
9. [F] FRIEDMAN, A.: The Stefan problem in several space variables. Trans. Amer. Math. Soc. 133, 51-87 (1968)
10. [FK] FRIEDMAN, A., KINDERLEHRER, D.: A one phase Stefan problem. Indiana Univ. Math. J. 24, 1005-1035 (1975)
11. [GT] GILBARG, D., TRUDINGER, N.: Elliptic partial differential equations of second order. Springer-Verlag, Berlin/New York, 1977
12. [H] HANZAWA, E.: Classical solutions of the Stefan problem. Tohoku Math. J. 33, 297-335 (1981)
13. [K] KAMENOMOSTSKAJA, S.L.: On Stefan's problem. Mat. Sb. 53, 489-514 (1961), (in Russian)
14. [O] OLEINIK, O.A.: A method of solution of the general Stefan problem. Soviet Math. Dokl. 1, 1350-1354 (1960)