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The n-dimensional analogue of the catenary:
existence and nonexistence
Ulrich Dierkes and Gerhard Huisken |
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Vol. 141 (1990), No. 1, 47–54
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Abstract |
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We study “heavy” n-dimensional surfaces suspended from some prescribed (n − 1)-dimensional boundary data. This leads to a mean curvature type equation with a non-monotone right hand side. We show that the equation has no solution if the boundary data are too small, and, using a fixed point argument, that the problem always has a smooth solution for sufficiently large boundary data. |
Mathematical Subject Classification 2000
Primary: 49F10
Secondary: 53A10
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Milestones
Received: 15 January 1988
Published: 1 January 1990
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Authors |
| Ulrich Dierkes | |
| Gerhard Huisken | |
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