A New Proof of the Interior Gradient Bound for the Minimal Surface Equation in n Dimensions

1 April 1972

journal article
Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences

Vol. 69 (4) , 821-823
https://doi.org/10.1073/pnas.69.4.821

Abstract

An interior gradient bound for classical solutions of the minimal surface equation in n variables was established by Bombieri, De Giorgi, and Miranda in 1968. We provide a new and simpler derivation of this estimate and partly develop in the process some new techniques applicable to the study of hypersurfaces in general.

Keywords

INTERIOR GRADIENT
GRADIENT BOUND
SURFACE EQUATION
MINIMAL SURFACE
CLASSICAL SOLUTIONS
NEW TECHNIQUES
PARTLY DEVELOP
TECHNIQUES APPLICABLE
SIMPLER DERIVATION

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