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The differential equation $ \Delta x=2H(x\sb{u}\wedge x\sb{v})$ with vanishing boundary values


Author: Henry C. Wente
Journal: Proc. Amer. Math. Soc. 50 (1975), 131-137
MSC: Primary 35J65; Secondary 49F10
DOI: https://doi.org/10.1090/S0002-9939-1975-0374673-1
MathSciNet review: 0374673
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Abstract: If $ x(u,v)$ is a solution to the system $ \Delta x = 2H({x_u} \wedge {x_v})$ on a bounded domain $ G \subset {R^2}$ with finite Dirichlet integral and with $ x = 0$ on $ \partial G$, then $ x \equiv 0$ for simply connected $ G$, but for doubly-connected $ G$ we construct nontrivial solutions.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0374673-1
Keywords: Dirichlet integral, constant mean curvature, oriented volume functional
Article copyright: © Copyright 1975 American Mathematical Society

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