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

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Issue Date
2008
Authors
Jin, Zhiren
Advisor
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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