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A necessary condition of solvability for the capillarity boundary of Monge-Ampere equations in two dimensions
Author(s):
Ma
Xi-Nan
Journal:
Proc. Amer. Math. Soc.
127
(1999),
763-769.
MSC (1991):
Primary 35J25, 35J60, 35J65;
Secondary 53C45
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.
References:
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- 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
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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:
10.1090/S0002-9939-99-04750-4
PII:
S 0002-9939(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
Copyright of article:
Copyright
1999,
American Mathematical Society
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