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


Author: Ma Xi-Nan
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
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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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  • 1. L.Caffarelli, L.Nirenberg and J.Spruck, The Dirichlet Problem for Nonlinear Second-Order Elliptic Equations I.Monge-Ampere Equation, Comm. Pure App. Math. 37 (1984), 369-402. MR 88k:35073
  • 2. P.L.Lions, N.S.Trudinger and J.Urbas, The Neumann problem for equations of Monge-Ampere type, Comm. Pure Appl. Math. 39 (1986), 539-563. MR 87j:35114
  • 3. Ma Xi-nan, Isoperimetric bounds for Monge-Ampere equations in two dimensions, to appear in Analysis.
  • 4. R.P.Sperb, Maximum Principles and Their Applications, Academic Press,New York, 1981. MR 84a:35033
  • 5. N.S.Trudinger, On degenerate fully nonlinear ellptic equations in balls, Bull. Aust. Math. Soc. 111 (1987), 299-307. MR 88b:35083
  • 6. J.Urbas, The oblique derivative problem for equations of Monge-Ampere type, Proceeding of the Centre for Mathematical Analysis, Australian National University 12 (1987), 171-195. MR 89b:35045
  • 7. J.Urbas, Nonlinear oblique boundary value problem for Hessian equations in two dimensions, Ann. Inst. Henri Poincare 12 (1995), 507-575. MR 96h:35071

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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

DOI: https://doi.org/10.1090/S0002-9939-99-04750-4
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

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