On the twice differentiability of viscosity solutions of nonlinear elliptic equations
- 1 June 1989
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 39 (3) , 443-447
- https://doi.org/10.1017/s0004972700003361
Abstract
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.Keywords
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