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Smoothness of the solution of the trivial Monge-Ampère equation

Published online by Cambridge University Press:  17 April 2009

Vitaly Ushakov
Vitaly Ushakov
Affiliation:
Department of MathematicsThe University of MelbourneParkville Vic 3052Australia e-mail: vit@mundoe.maths.mu.oz.au
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Abstract

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A solution of the equation must be C2 smooth, need not be C3 smooth, but at the same time the ratio zxy: zxx is C1 (provided zxx ≠ 0). An analytical proof of this fact is given; the underlying geometrical interpretation is discussed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 439 - 445
Copyright
Copyright © Australian Mathematical Society 1997

References

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