Interior gradient bounds for the mean curvature equation by viscosity solutions methods (Q1174555)

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scientific article; zbMATH DE number 9032
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Interior gradient bounds for the mean curvature equation by viscosity solutions methods
scientific article; zbMATH DE number 9032

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    Interior gradient bounds for the mean curvature equation by viscosity solutions methods (English)
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    25 June 1992
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    This interesting paper gives a new proof of gradient estimates for solutions of the prescribed mean curvature equation via viscosity solutions methods. The usual proof for interior gradient bounds is based on works of \textit{E. Bombieri}, \textit{E. De Giorgi} and \textit{M. Miranda} [Arch. Ration. Mech. Anal. 32, 255--267 (1969; Zbl 0184.32803)] and use sophisticated test function arguments. The author avoids such arguments as did \textit{N. Korevaar} [Proc. Symp. Pure Math. 45, Pt. 2, 81--89 (1986; Zbl 0599.35046)] via a still different approach. Unfortunately, Korevaar's paper is not listed in the references.
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    gradient estimates
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    prescribed mean curvature equation
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    viscosity solutions
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