A Remark on the Characterization of the Gradient of a Distribution

Xiaoming Wang

doi:10.1080/00036819308840202

A Remark on the Characterization of the Gradient of a Distribution

Xiaoming Wang

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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. © 1993, Taylor & Francis Group, LLC. All rights reserved.

Original language	American English
Journal	Applicable Analysis
Volume	51
DOIs	https://doi.org/10.1080/00036819308840202
State	Published - Dec 1 1993

Keywords

Distribution
Test Function

Disciplines

Mathematics
Statistics and Probability

Access to Document

10.1080/00036819308840202License: Unspecified

https://doi.org/10.1080/00036819308840202

Cite this

@article{eee8e2fc1c384c57a24efb0aa856ca5f,

title = "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. {\textcopyright} 1993, Taylor \& Francis Group, LLC. All rights reserved.",

keywords = "Distribution, Test Function",

author = "Xiaoming Wang",

year = "1993",

month = dec,

day = "1",

doi = "10.1080/00036819308840202",

language = "American English",

volume = "51",

journal = "Applicable Analysis",

}

TY - JOUR

T1 - A Remark on the Characterization of the Gradient of a Distribution

AU - Wang, Xiaoming

PY - 1993/12/1

Y1 - 1993/12/1

N2 - 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. © 1993, Taylor & Francis Group, LLC. All rights reserved.

AB - 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. © 1993, Taylor & Francis Group, LLC. All rights reserved.

KW - Distribution

KW - Test Function

UR - https://scholarsmine.mst.edu/math_stat_facwork/1271

UR - https://doi.org/10.1080/00036819308840202

U2 - 10.1080/00036819308840202

DO - 10.1080/00036819308840202

M3 - Article

VL - 51

JO - Applicable Analysis

JF - Applicable Analysis

ER -

A Remark on the Characterization of the Gradient of a Distribution

Abstract

Keywords

Disciplines

Access to Document

Other files and links

Fingerprint

Cite this