Table of Contents
ISRN Mathematical Physics
Volume 2012, Article ID 973968, 7 pages
Research Article

Green's Second Identity for Vector Fields

Laboratorio de Óptica Cuántica, Departamento de Física, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 México, DF, Mexico

Received 2 May 2012; Accepted 20 June 2012

Academic Editors: U. Kulshreshtha, P. Roy, and D. Singleton

Copyright © 2012 M. Fernández-Guasti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The second derivative of two vector functions is related to the divergence of the vector functions with first order operators. Namely, 𝐏 β‹… βˆ‡ 2 𝐐 βˆ’ 𝐐 β‹… βˆ‡ 2 𝐏 = βˆ‡ β‹… [ 𝐏 ( βˆ‡ β‹… 𝐐 ) βˆ’ 𝐐 ( βˆ‡ β‹… 𝐏 ) + 𝐏 Γ— βˆ‡ Γ— 𝐐 βˆ’ 𝐐 Γ— βˆ‡ Γ— 𝐏 ] .