DIFFERENTIABILITY PROPERTIES OF ORLICZ-SOBOLEV FUNCTIONS ON METRIC MEASURE SPACES

摘要

Given a metric measure space (X,d,μ) and a Young function Φ : [0,∞) → [0,∞), we prove two differentiability results for functions in the Orlicz-Sobolev space N 1,Φ (X). The first result uses a characterization of approximate differentiability of real functions defined on a complete doubling metric measure space, proved by A. Durand-Cartagena, L. Ihnatsyeva, R. Korte and M. Szuma′ nska (2014) and generalizes the approximate dif- ferentiability of Newtonian functions. The second result extends to the metric setting a result of A. Alberico and A. Cianchi (2005) proving the a.e. differentiability of Orlicz- Sobolev functions from W 1,Φ loc (?), where ? ? R n is an open set and Φ satisfies a certain Calderón-type growth condition.