Kato's inequality when Δ u is a measure

Abstract

We extend the classical version of Kato's inequality in order to allow functions u∈ L 1 loc such that Δ u is a Radon measure. This inequality has been recently applied by Brezis, Marcus, and Ponce to study the existence of solutions of the nonlinear equation −Δ u+ g( u)= μ, where μ is a measure and g : R→ R is a nondecreasing continuous function. To cite this article: H. Brezis, A.C. Ponce, C. R. Acad. Sci. Paris, Ser. I 338 (2004).