Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T02:07:42.779Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected])
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)