Electron. J. Diff. Eqns.,
Vol. 2008(2008), No. 24, pp. 115.
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
().
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
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 boundaryvalue 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 672600033, USA
email: zhiren@math.wichita.edu 
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