### Abstract

In this paper we show that if the Lipschitz constant of the initial free boundary is small, then for small positive time the solution is smooth and satisfies the Hele-Shaw equation in the classical sense. A key ingredient in the proof which is of independent interest is an estimate up to order of magnitude of the speed of the free boundary in terms of initial data.

Original language | English (US) |
---|---|

Pages (from-to) | 527-582 |

Number of pages | 56 |

Journal | American Journal of Mathematics |

Volume | 129 |

Issue number | 2 |

State | Published - Apr 2007 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*American Journal of Mathematics*,

*129*(2), 527-582.

**Regularity for the one-phase hele-shaw problem from a lipschitz initial surface.** / Choi, Sunhi; Jerison, David; Kim, Inwon.

Research output: Contribution to journal › Article

*American Journal of Mathematics*, vol. 129, no. 2, pp. 527-582.

}

TY - JOUR

T1 - Regularity for the one-phase hele-shaw problem from a lipschitz initial surface

AU - Choi, Sunhi

AU - Jerison, David

AU - Kim, Inwon

PY - 2007/4

Y1 - 2007/4

N2 - In this paper we show that if the Lipschitz constant of the initial free boundary is small, then for small positive time the solution is smooth and satisfies the Hele-Shaw equation in the classical sense. A key ingredient in the proof which is of independent interest is an estimate up to order of magnitude of the speed of the free boundary in terms of initial data.

AB - In this paper we show that if the Lipschitz constant of the initial free boundary is small, then for small positive time the solution is smooth and satisfies the Hele-Shaw equation in the classical sense. A key ingredient in the proof which is of independent interest is an estimate up to order of magnitude of the speed of the free boundary in terms of initial data.

UR - http://www.scopus.com/inward/record.url?scp=34248545694&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34248545694&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:34248545694

VL - 129

SP - 527

EP - 582

JO - American Journal of Mathematics

JF - American Journal of Mathematics

SN - 0002-9327

IS - 2

ER -