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On second derivative estimates for equations of Monge-Ampère type

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, G.P.O. Box 4 Canberra A.C.T. 2601, Australia.
John I.E. Urbas
Affiliation:
Centre for Mathematical Analysis, Australian National University, G.P.O. Box 4 Canberra A.C.T. 2601, Australia.
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Abstract

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We derive interior second derivative estimates for solutions of equations of Monge-Ampère type which extend those of Pogorelov for the case of affine boundary values. A key ingredient in our method is the existence of a strong solution of the homogeneous Monge-Ampère equation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 30 , Issue 3 , December 1984 , pp. 321 - 334
Copyright
Copyright © Australian Mathematical Society 1984

References

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