Electron. J. Diff. Eqns., Vol. 2008(2008), No. 24, pp. 1-15.

Growth rate and existence of solutions to Dirichlet problems for prescribed mean curvature equations on unbounded domains

Zhiren Jin

Abstract:
We prove growth rate estimates and existence of solutions to Dirichlet problems for prescribed mean curvature equation on unbounded domains inside the complement of a cone or a parabola like region in $\mathbb{R}^n$ ($n\geq 2$). The existence results are proved using a modified Perron's method by which a subsolution is a solution to the minimal surface equation, while the role played by a supersolution is replaced by estimates on the uniform $C^{0}$ bounds on the liftings of subfunctions on compact sets.

Submitted February 9, 2008. Published February 22, 2008.
Math Subject Classifications: 35J25, 35J60, 35J65.
Key Words: Elliptic boundary-value problem; quasilinear elliptic equation; prescribed mean curvature equation; unbounded domain; Perron's method

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Zhiren Jin
Department of Mathematics and Statistics
Wichita State University
Wichita, Kansas 67260-0033, USA
email: zhiren@math.wichita.edu

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