Solution of Laplace’s Equation in A Singular Domain Using Mellin Transform

Sami Altoum; Ahmed Hussein Msmali; Mahjoub A. Elamin

doi:10.22342/jims.28.2.1052.107-121

Sami Altoum ⁽¹⁾ , Ahmed Hussein Msmali ⁽²⁾ , Mahjoub A. Elamin ⁽³⁾

(1) Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, KSA, Saudi Arabia,

(2) Mathematics Department, Jazan University, Saudi Arabia,

(3) Department of Mathematics, University College of Umluj, Tabuk University, Saudi Arabia

https://doi.org/10.22342/jims.28.2.1052.107-121

Issue
VOLUME 28 NUMBER 2 (JULY 2022)

Submitted
September 27, 2021

Accepted
April 7, 2022

Published
July 27, 2022

Keywords:

Mellin transform, Laplace’s equation, Regularity, Singularity.

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Abstract

This paper deals with the theory of V. Kondratiev which allows to study the regularity of elliptical problems in corner domains. After having introduced the Mellin transform and the Sobolev spaces to weight, we recall the links with Sobolev spaces. The Mellin transform represent an important key to study the H^s regularity in corner domains.

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References

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Authors

Sami Altoum

Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, KSA

shtoum@uqu.edu.sa (Primary Contact)

Ahmed Hussein Msmali

Mathematics Department, Jazan University

Mahjoub A. Elamin

Department of Mathematics, University College of Umluj, Tabuk University

Altoum, S., Msmali, A. H., & Elamin, M. A. (2022). Solution of Laplace’s Equation in A Singular Domain Using Mellin Transform. Journal of the Indonesian Mathematical Society, 28(2), 107–121. https://doi.org/10.22342/jims.28.2.1052.107-121