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Existence of solutions of the prescribed mean-curvature equation on unbounded domains

Published online by Cambridge University Press:  12 July 2007

Zhiren Jin
Zhiren Jin
Affiliation:
Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67260-0033, USA (zhiren@math.wichita.edu)
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Abstract

The existence of solutions of the Dirichlet problems for the prescribed mean-curvature equation on some unbounded domains in Rn(n ≥ 2) is proved. The results are proved using a modified version of the Perron method, where a subsolution is a solution to the minimal surface equation, while a supersolution is not constructed; instead, the role played by a supersolution is replaced by the estimates on the uniform bounds on the liftings of subfunctions on compact sets.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 1 , February 2006 , pp. 157 - 179
Copyright
Copyright © Royal Society of Edinburgh 2006

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