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

Sunhi Choi, David Jerison, Inwon Kim

Research output: Contribution to journalArticle

14 Scopus citations

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 languageEnglish (US)
Pages (from-to)527-582
Number of pages56
JournalAmerican Journal of Mathematics
Volume129
Issue number2
DOIs
StatePublished - Apr 2007

ASJC Scopus subject areas

  • Mathematics(all)

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