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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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