A necessary condition of solvability
for the capillarity boundary
of Monge-Ampere equations in two dimensions
Abstract: 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.
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Affiliation: Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China
Keywords: Monge-Ampere equation, maximum principle, curvilinear coordinate system, contact angle boundary
Received by editor(s): June 16, 1997
Communicated by: Peter Li
Article copyright: © Copyright 1999 American Mathematical Society