A free boundary problem with optimal transportation
A free boundary problem with optimal transportation
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最优运输的自由边界问题
DOI：
10.1002/cpa.3041
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发表时间：
2004
影响因子：
3
通讯作者：
O. Savin
中科院分区：
文献类型：
--
作者：
O. Savin
Bernis 和 Friedman [4]、Bernis [3]、Bertozzi 和 Pugh [5]、Otto [12, 13] 等人在一维情况下研究了该方程。在[3]中，Bernis 证明非负解具有有限的传播速度，并且分隔 {u > 0} 和 {u = 0} 的自由边界是 Holder 连续的。在[13]中，Otto 使用上述时间离散格式证明了具有指定接触角的润滑方程的存在性，其能量泛函 E(u) = |{u > 0}| + ∫ (u′)2。在本文中，我们将研究“离散润滑方程”，即以下变分问题的解：
This equation was studied in the one-dimensional case by Bernis and Friedman [4], Bernis [3], Bertozzi and Pugh [5], Otto [12, 13], and others. In [3] Bernis proved that nonnegative solutions have finite speed of propagation and the free boundary separating {u > 0} and {u = 0} is Holder-continuous. In [13] Otto showed existence of the lubrication equation with prescribed contact angle using the above time-discrete scheme with the energy functional E(u) = |{u > 0}| + ∫ (u′)2. In this paper we are going to study the “discrete lubrication equation,” that is, the solution of the following variational problem: