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

D. Choi, David Jerison, Inwon C. Kim

• 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