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

@inproceedings{Choi2007RegularityFT,
title={Regularity for the one-phase Hele-Shaw problem from a Lipschitz initial surface},
author={H Choi},
year={2007}
}

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. 0. Introduction. Consider a compact set K ⊂ Rn with smooth boundary ∂K. Suppose that a bounded domain Ω contains K and let Ω0… CONTINUE READING