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Growth rate and existence of solutions to Dirichlet problems for prescribed mean curvature equations on unbounded domains
Jin, Zhiren
Jin, Zhiren
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2008
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Article
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Keywords
Elliptic boundary-value problem,Quasilinear elliptic equation,Prescribed mean curvature equation,Unbounded domain,Perron’s method
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Citation
Jin, Zhiren. Growth rate and existence of solutions to Dirichlet problems for prescribed mean curvature equations on unbounded domains. Electronic Journal of Differential Equations. Vol. 2008(2008), No. 24, pp. 1-15.
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 Rn (n 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 C0 bounds on the
liftings of subfunctions on compact sets.
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Click on the link to access this article for free at the publisher's website: http://ejde.math.unt.edu/Volumes/2008/24/jin.pdf
Publisher
Texas State University - San Marcos
Journal
Electronic Journal of Differential Equations
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ISSN
1072-6691