Regularity for the one-phase Hele-Shaw problem from a Lipschitz initial surface

• Autores: D. Choi, David Jerison, Inwon C. Kim
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 129, Nº 2, 2007, págs. 527-582
• Idioma: inglés
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• Resumen

  • 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