Regularity for the one-phase hele-shaw problem from a lipschitz initial surface

American Journal of Mathematics

Volumn 129, Issue 2, 2007, Pages 527-582

  Choi, Sunhi ^a   Jerison, David ^a   Kim, Inwon ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34248545694     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.2007.0008     Document Type: Article

References (17)

1. I. Athanasopoulos, L. Caffarelli and S. Salsa, Regularity of the free boundary in parabolic phasetransition problems, Acta Math. 176 (1996), 245-282.
2. 1,α Rev. Mat. Iberoamericana 3 (1987), no. 2, 139-162.
3. 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.
4. B. Dahlberg, Harmonic functions in Lipschitz domains. Harmonic analysis in Euclidean spaces, Proc. Sympos. Pure Math., vol. XXXV, Part 1, Amer. Math. Soc., Providence, RI, 1979, pp. 313-322.
5. 1 domains. Studio Math. 66 (1979), 13-24.
6. C. M. Elliot and V. Janovsky, A variational inequality approach to Hele-Shaw flow with a moving boundary, Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), nos. 1-2, 93-107.
7. J. Escher and G. Simonett, Classical solutions of multidimensional Hele-Shaw models, SIAM J. Math. Anal. 28 (1997), no. 5, 1028-1047.
8. H. Helson and G. Szegö, A problem in prediction theory, Ann. Mat. Pura. Appl. (4) 51 (1960), 107-138.
9. R. Hunt, B. Muckenhoupt and R. Wheeden, Weighted norm inequalities for the conjugate function and Hubert transform, Trans. Amer. Math. Soc. 176 (1973), 227-251.
10. D. S. Jerison and C. E. Kenig, Boundary behavior of Harmonic functions in Non-tangentially Accessible Domains, Adv. Math. 46 (1982), 80-147.
11. 1 domain has vanishing mean oscillation, Trans. Amer. Math. Soc. 273 (1982), 781-794.
12. _, Boundary value problems on Lipschitz domains, Studies in Partial Differential Equations (W. Littman, ed.), Math. Assoc. Amer., 1982, pp. 1-68.
13. D. S. Jerison and I. Kim, The one-phase Hele-Shaw problem with singularities, J. Geom. Anal. 15 (2005), 641-667.
14. I. Kim, Uniqueness and Existence result of Hele-Shaw and Stefan problem, Arch. Rat. Mech. Anal. 168 (2003), 299-328.
15. _, Regularity of free boundary in one phase Hele-Shaw problem, J. Differential Equations 223 (2006), 161-184.
16. J. R. King, A. A. Lacey and J. L. Vazquez, Persistence of corners in free boundaries in Hele-Shaw flow, Euro. J. Appl. Math. 6 (1995), 455-490.
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), 17-37.