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Transactions of the American Mathematical Society

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Boundary behavior of a nonparametric surface of prescribed mean curvature near a reentrant corner


Authors: Alan R. Elcrat and Kirk E. Lancaster
Journal: Trans. Amer. Math. Soc. 297 (1986), 645-650
MSC: Primary 35J60
MathSciNet review: 854090
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Abstract: Let $ \Omega $ be an open set in $ {{\mathbf{R}}^2}$ which is locally convex at each point of its boundary except one, say $ (0,0)$. Under certain mild assumptions, the solution of a prescribed mean curvature equation on $ \Omega $ behaves as follows: All radial limits of the solution from directions in $ \Omega $ exist at $ (0,0)$, these limits are not identical, and the limits from a certain half-space $ (H)$ are identical. In particular, the restriction of the solution to $ \Omega \cap H$ is the solution of an appropriate Dirichlet problem.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0854090-X
Article copyright: © Copyright 1986 American Mathematical Society