caa a22 4500 386360588 CHVBK 20180307111913.0 cr unu---uuuuu 161130e198906 xx s 000 0 eng 10.1017/S0004972700003361 doi S0004972700003361 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700003361 Trudinger Neil S. Centre for Mathematical Analysis, Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601. On the twice differentiability of viscosity solutions of nonlinear elliptic equations [Elektronische Daten] [Neil S. Trudinger] 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. Copyright © Australian Mathematical Society 1989 Bulletin of the Australian Mathematical Society Cambridge University Press 39/3(1989-06), 443-447 0004-9727 39:3<443 1989 39 BAZ https://doi.org/10.1017/S0004972700003361 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700003361 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Trudinger Neil S. Centre for Mathematical Analysis, Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601 NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 39/3(1989-06), 443-447 0004-9727 39:3<443 1989 39 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge