## A necessary condition of solvability for the capillarity boundary of Monge-Ampere equations in two dimensions

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- Proc. Amer. Math. Soc.
**127**(1999), 763-769 Request permission

## 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.## References

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## Additional Information

**Ma Xi-Nan**- Affiliation: Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China
- Email: xnma@math.ecnu.edu.cn
- Received by editor(s): June 16, 1997
- Communicated by: Peter Li
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**127**(1999), 763-769 - MSC (1991): Primary 35J25, 35J60, 35J65; Secondary 53C45
- DOI: https://doi.org/10.1090/S0002-9939-99-04750-4
- MathSciNet review: 1487323