Regularity of the free boundary for the one phase Hele-Shaw problem

Journal of Differential Equations

Volumn 223, Issue 1, 2006, Pages 161-184

  Kim, Inwon C ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33644745127     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2005.07.003     Document Type: Article

References (18)

1. S.B. Angenent Nonlinear analytic semiflows Proc. Roy. Soc. Edinburgh 115A 1990 91-107
2. S.N. Antontsev C.R. Gonalves A.M. Meirmanov Local existence of classical solutions to the well-posed Hele-Shaw problem Port. Math. (N.S.) 59 2002 435-452
3. I. Athanasopoulos L. Caffarelli S. Salsa Regularity of the free boundary in parabolic phase-transition problems Acta Math. 176 1996 245-282
4. L. Caffarelli The regularity of free boundaries in higher dimension Acta Math. 139 1977 155-184
5. 1,α Rev. Mat. Iberoamericana 3 2 1987 139-162
6. L. Caffarelli A Harnack inequality approach to the regularity of free boundaries, Part II: Flat free boundaries are Lipschitz Comm. Pure Appl. Math. 42 1989 55-78
7. S. Choi, D. Jerison, I. Kim, Regularity for one-phase Hele-Shaw problem from a Lipschitz initial surface, submitted.
8. B.E. Dahlberg, Harmonic functions in Lipschitz domains, Harmonic analysis in Euclidean Spaces, Part 1, pp. 313-322, Proceedings of the Symposium Pure Mathematics, vol. XXXV, Part, American Mathematical Society, Providence, RI, 1979.
9. P. Daskalopoulos K. Lee All time smooth solutions of the one-phase Stefan problem and the Hele-Shaw flow Comm. Partial Differential Equations 29 2004 71-89
10. C.M. Elliot V. Janovsky A variational inequality approach to Hele-Shaw flow with a moving boundary Proc. Roy. Soc. Edinburgh Sect. A 88 1-2 1981 93-107
11. J. Escher G. Simonett Classical solutions of multidimensional Hele-Shaw models SIAM J. Math. Anal. 28 5 1997 1028-1047
12. A. Friedman Variational principles and free boundary problems, Pure and Applied Mathematics 1982 Wiley New York
13. D.S. Jerison C.E. Kenig Boundary value problems on Lipschitz domains W. Littman Studies in Partial Differential Equations 1982 The Mathematical Association of America 1-68
14. I.C. Kim Uniqueness and existence result of Hele-Shaw and Stefan problem Arch. Rational Mech. Anal. 168 2003 299-328
15. I.C. Kim, Long time regularity of Hele-Shaw problem, submitted.
16. D. Kinderlehrer L. Nirenberg Hodograph methods and the smoothness of the free boundary in the one phase Stefan problem D.G. Wilson A.D. Solomon P.T. Boggs Moving Boundary Problems 1978 Academic Press New York 57-69
17. A.M. Meirmanov B. Zaltzman Global in time solution to the Hele-Shaw problem with a change of topology European J. Appl. Math. 13 2002 431-447
18. K.-O. Widman Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations Math. Scand. 21 1967 17-37