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Proceedings of the American Mathematical Society

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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.
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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