A NECESSARY CONDITION OF SOLVABILITY FOR THE CAPILLARITY BOUNDARY OF MONGE-AMPERE EQUATIONS IN TWO DIMENSIONS
A NECESSARY CONDITION OF SOLVABILITY FOR THE CAPILLARITY BOUNDARY OF MONGE-AMPERE EQUATIONS IN TWO DIMENSIONS
复制标题
二维蒙安方程毛细管边界可解的必要条件
DOI：
10.1090/s0002-9939-99-04750-4
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
Ma Xin
中科院分区：
文献类型：
--
作者：
Ma Xin
本文考虑二维有界严格凸域上一类具有给定接触角的Monge-Ampere方程边值问题。目的是给出上述方程可解的一个精确必要条件。这是通过使用最大值原理并引入二维Monge-Ampere方程的曲线坐标系来实现的。我们的必要条件的一个有趣的特征是在区域边界的曲率和边界条件之间需要一定的强限制，这在Dirichlet和Neumann边值中没有出现。？
In this paper we consider a class of Monge-Ampere equations with a prescribed contact angle boundary value problem on a bounded strictly convex domain in two dimensions. The purpose is to give a sharp necessary condition of solvability for the above mentioned equations. This is achieved by using the maximum principle and introducing a curvilinear coordinate system for Monge-Ampere equations in two dimensions. An interesting feature of our necessary condition is the need for a certain strong restriction between the curvature of the boundary of domain and the boundary condition, which does not appear in the Dirichlet and Neumann boundary values. ?