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ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 63, Issue 2, pp 249–276 | Cite as

Explicit div-curl inequalities in bounded and unbounded domains of \({{\mathbb {R}}}^3\)

  • Tahar Zamene Boulmezaoud
  • Keltoum Kaliche
  • Nabil Kerdid
Article

Abstract

We give a constructive proof of some functional inequalities related to the div and curl operators in bounded and unbounded domains of \({{\mathbb {R}}}^3\). Our new innovation consists in giving explicit constants in several geometric configurations. These inequalities are of a first use in solving div-curl systems and vector potential problems arising in physics.

Keywords

Div-curl systems Div-curl inequalities Vector potentials Weighted inequalities Unbounded domains 

Mathematics Subject Classification

35Q60 35Q61 35B45 35F45 

Notes

Acknowledgments

The authors would like to thank the anonymous reviewer for careful and thorough reading of this manuscript, and for helpful and valuable comments, which significantly contributed to improving the quality of this publication.

The third author, N. Kerdid, gratefully acknowledge the support of the National Plan for Science, Technology and Information (Maarifah), King Abdulaziz City for Science and Technology, KSA, award number 12-MAT2996-08.

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Copyright information

© Università degli Studi di Ferrara 2016

Authors and Affiliations

  • Tahar Zamene Boulmezaoud
    • 1
  • Keltoum Kaliche
    • 1
  • Nabil Kerdid
    • 2
  1. 1.Laboratoire de Mathématiques de VersaillesUVSQ, CNRS, Université Paris-SaclayVersaillesFrance
  2. 2.College of Sciences, Department of Mathematics and Statistics, Al Imam Mohammad Ibn Saud University (IMSIU)RiyadhKingdom of Saudi Arabia

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