Regularity for the one-phase Hele-Shaw problem from a Lipschitz initial surface
Regularity for the one-phase Hele-Shaw problem from a Lipschitz initial surface
复制标题
Lipschitz 初始表面的单相 Hele-Shaw 问题的正则性
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
Inwon C. Kim
中科院分区：
文献类型：
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作者：
Sunhi Choi;D. Jerison;Inwon C. Kim
本文证明了当初始自由边界的Lipschitz常数很小时，对于小的正时间，解是光滑的，并且满足经典意义下的Hele-Shaw方程.在证明这是独立的利益的一个关键因素是一个估计的数量级的自由边界的速度在初始数据。
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.