Kato’s inequality for the strong $p(\cdot )$-Laplacian

Abstract

wherein the sense of distributions for a certain exponent p ∈ C 1 (Ω) with 1 < p − < p + < ∞ and for functions u belonging to an admissible class. This extends the well-known Kato's inequality for strongly elliptic second-order differential operators to the strong p(•)-Laplacian.