Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 24, pp. 1-15.
Title: Growth rate and existence of solutions to Dirichlet problems for
prescribed mean curvature equations on unbounded domains
Author: Zhiren Jin (Wichita State Univ., Kansas, USA)
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