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VOL. 10 | 1986 Some fully non-linear parabolic partial differential equations


In this paper I wish to discuss the classical solvability of the first boundary value problem for a class of non-linear parabolic equations of second order. The equations to be considered arise from symmetric functions in a natural way analagous to the equations considered by Caffarelli, Nirenberg and Spruck [CNS] in the elliptic case. They are also motivated by the proposed analogue of the Monge-Ampère equation of Krylov [KL which is considered here as a first special case. I do not present the proofs of the results described, but only rough indications of the methods involved. The work constitutes the central results of the latter half of my doctoral dissertation [R l]


Published: 1 January 1986
First available in Project Euclid: 18 November 2014

zbMATH: 0599.35082
MathSciNet: MR857666

Rights: Copyright © 1986, Centre for Mathematical Analysis, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.


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