The Dirichlet problem for the equation of prescribed Gauss curvature

1 October 1983

journal article
research article
Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society

Vol. 28 (2) , 217-231
https://doi.org/10.1017/s000497270002089x

Abstract

We treat necessary and sufficient conditions for the classical solvability of the Dirichlet problem for the equation of prescribed Gauss curvature in uniformly convex domains in Euclidean n space. Our methods simultaneously embrace more general equations of Monge-Ampère type and we establish conditions which ensure that solutions have globally bounded second derivatives.

Keywords

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