A remark on the characterization of the gradient of a distribution

Abstract

It is shown in this paper that a scalar test function in Rⁿ is the divergence of a vector valued test function if and if its integral over the domain vanishes. Using this result, we are able to give an elementary proof of the characterization of the gradient of a distribution. Also an application on characterization of the curl of a distribution in R² is presented.

Keywords:

• Test function
• distribution