Publication Cover
Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 2
119
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Regularization using different surfaces and the second-order derivatives of 1/r

&
Pages 246-258 | Received 07 Apr 2011, Accepted 21 Jul 2011, Published online: 14 Sep 2011

References

  • Estrada , R and Fulling , SA . 2002 . How singular functions define distributions . J. Phys. A , 35 : 3079 – 3089 .
  • Hnizdo , V . 2011 . Generalized second-order partial derivatives of 1/r . Eur. J. Phys. , 32 : 287 – 297 .
  • Farassat , F . Introduction to generalized functions with applications in aerodynamics and aeroacoustics, NASA Technical Paper 3248, NASA Langley Research Center, Hampton, VA, 1996. Available at http://ntrs.nasa.gov
  • Frahm , CP . 1983 . Some novel delta-function identities . Am. J. Phys. , 51 : 826 – 829 .
  • Estrada , R and Kanwal , RP . 1985 . Regularization and distributional derivatives of in 𝒟′(ℝ p ) . Proc. R. Soc. Lond. A , 401 : 281 – 297 .
  • Estrada , R and Kanwal , RP . 1989 . Regularization, pseudofunction, and Hadamard finite part . J. Math. Anal. Appl. , 141 : 195 – 207 .
  • Estrada , R and Kanwal , RP . 2002 . “ A Distributional Approach to Asymptotics ” . In , Theory and Applications , 2nd , Boston : Birkhäuser .
  • Kanwal , RP . 2004 . Generalized Functions: Theory and Technique , 3rd , Boston : Birkhäuser .
  • Gsponer , A . 2007 . Distributions in spherical coordinates with applications to classical electrodynamics . Eur. J. Phys. , 28 : 267 – 275 . Eur. J. Phys. 28 (2007), p. 1241 (corrigendum)
  • Franklin , J . Comment on ‘Some novel delta-function identities, by Charles P. Frahm (Am. J. Phys. 51 (1983), pp. 826–829), Am. J. Phys. 78 (2010), pp. 1225–1226
  • Blanchet , L and Faye , G . 2000 . Hadamard regularization . J. Math. Phys. , 41 : 7675 – 7714 .
  • Blinder , SM . 2003 . Delta functions in spherical coordinates and how to avoid losing them: Fields of point charges and dipoles . Am. J. Phys. , 71 : 816 – 818 .
  • Estrada , R and Fulling , SA . 2007 . Spaces of test functions and distributions in spaces with thick points . Int. J. Appl. Math. Stat. , 10 : 25 – 37 .
  • Hnizdo , V . 2000 . On the Laplacian of 1/r . Eur. J. Phys. , 21 : L1 – L3 .
  • Estrada , R and Kanwal , RP . 1990 . A distributional theory for asymptotic expansions . Proc. R. Soc. Lond. A , 428 : 399 – 430 .
  • Spivak , M . A Comprehensive Introduction to Differential Geometry, 3rd ed. with corrections, Vol. 1, Publish or Perish, Inc., Houston, TX, 2005

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.