DIFFERENTIABILITY OF MONOTONE SOBOLEV FUNCTIONS ON METRIC SPACES
MARCELINA MOCANU “Vasile Alecsandri" University of Bacău, Faculty of Sciences Department of Mathematics, Informatics and Education Sciences Calea Mărăşeşti 157, Bacău 600115, ROMANIA
Corresponding author: mmocanu@ub.ro
We prove a differentiability result for monotone Sobolev functions on doubling metric measure spaces supporting a Poincaré inequality. This generalizes a result used by Rickman in proving the differentiability of quasiregular mappings. Our main tools are a Stepanov differentiability theorem in doubling metric measure spaces supporting a Poincaré inequality, proved in 2004 by Balogh, Rogovin and Zürcher and a Sobolev embedding theorem on spheres proved by Hajlasz and Koskela. As an application, it is shown that continuous quasiminimizers for the p- energy integral with p>Q-1 are almost everywhere Cheeger differentiable, where Q is the doubling expo-nent of the underlying metric measure space.
