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On the twice differentiability of viscosity solutions of nonlinear elliptic equations

Published online by Cambridge University Press:  17 April 2009

Neil S. Trudinger
Neil S. Trudinger
Affiliation:
Centre for Mathematical Analysis, Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601.
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Abstract

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We prove, under very general structure conditions, that continuous viscosity subsolutions of nonlinear second-order elliptic equations possess second order superdifferentials almost everywhere. Consequently we deduce the twice differentiability almost everywhere of viscosity solutions. The main idea of the proof is the backwards use of the Aleksandrov maximum principle as invoked in a previous work of Nadirashvili on sequences of solutions of linear elliptic equations.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 3 , June 1989 , pp. 443 - 447
Copyright
Copyright © Australian Mathematical Society 1989

References

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