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The Dirichlet problem for the equation of prescribed Gauss curvature

Published online by Cambridge University Press:  17 April 2009

Neil S. Trudinger  and
John I.E. Urbas
Neil S. Trudinger
Affiliation:
Centre for Mathematical Analysis, Australian National University, GPO Box 4, Canberra, ACT 2601, Australia.
John I.E. Urbas
Affiliation:
Centre for Mathematical Analysis, Australian National University, GPO Box 4, Canberra, ACT 2601, Australia.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 2 , October 1983 , pp. 217 - 231
Copyright
Copyright © Australian Mathematical Society 1983

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