We show that if Delta u is a finite measure in Omega then, under suitable assumptions on u near partial derivative Omega, Delta u(+) is also a finite measure in Omega. We also study properties of the normal derivatives partial derivative u/partial derivative n and partial derivative u(+)/partial derivative n on partial derivative Omega.
Brezis, H., & Ponce, A. (2008). Kato’s Inequality Up To the Boundary. Communications in Contemporary Mathematics, 10(6), 1217-1241. https://doi.org/10.1142/S0219199708003241 (Original work published 2008)