Boundary behavior of a nonparametric surface of prescribed mean curvature near a reentrant corner
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- by Alan R. Elcrat and Kirk E. Lancaster PDF
- Trans. Amer. Math. Soc. 297 (1986), 645-650 Request permission
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.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 297 (1986), 645-650
- MSC: Primary 35J60
- DOI: https://doi.org/10.1090/S0002-9947-1986-0854090-X
- MathSciNet review: 854090