On differentiability of Sobolev functions with respect to the Sobolev norm

Abstract

AbstractWe study connections between the ‐differentiability and the ‐differentiability of Sobolev functions. We prove that ‐differentiability implies the ‐differentiability, but the opposite implication is not valid. The notion of approximate differentiability is discussed as well. In addition, we consider the ‐differentiability of Sobolev functions ‐almost everywhere.