Singularities of Maxwell’s system in non-hilbertian Sobolev spaces

Wided Chikouche; Serge Nicaise

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2008)

  • Volume: 7, Issue: 3, page 455-482
  • ISSN: 0391-173X

Abstract

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We study the regularity of the solution of the regularized electric Maxwell problem in a polygonal domain with data in L p ( Ω ) 2 . Using a duality method, we prove a decomposition of the solution into a regular part in the non-Hilbertian Sobolev space W 2 , p ( Ω ) 2 and an explicit singular one.

How to cite

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Chikouche, Wided, and Nicaise, Serge. "Singularities of Maxwell’s system in non-hilbertian Sobolev spaces." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.3 (2008): 455-482. <http://eudml.org/doc/272260>.

@article{Chikouche2008,
abstract = {We study the regularity of the solution of the regularized electric Maxwell problem in a polygonal domain with data in $L^p(\Omega )^2$. Using a duality method, we prove a decomposition of the solution into a regular part in the non-Hilbertian Sobolev space $W^\{2,p\}(\Omega )^2$ and an explicit singular one.},
author = {Chikouche, Wided, Nicaise, Serge},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {two-dimensional Maxwell system; singularities in corners; polygonal domains},
language = {eng},
number = {3},
pages = {455-482},
publisher = {Scuola Normale Superiore, Pisa},
title = {Singularities of Maxwell’s system in non-hilbertian Sobolev spaces},
url = {http://eudml.org/doc/272260},
volume = {7},
year = {2008},
}

TY - JOUR
AU - Chikouche, Wided
AU - Nicaise, Serge
TI - Singularities of Maxwell’s system in non-hilbertian Sobolev spaces
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2008
PB - Scuola Normale Superiore, Pisa
VL - 7
IS - 3
SP - 455
EP - 482
AB - We study the regularity of the solution of the regularized electric Maxwell problem in a polygonal domain with data in $L^p(\Omega )^2$. Using a duality method, we prove a decomposition of the solution into a regular part in the non-Hilbertian Sobolev space $W^{2,p}(\Omega )^2$ and an explicit singular one.
LA - eng
KW - two-dimensional Maxwell system; singularities in corners; polygonal domains
UR - http://eudml.org/doc/272260
ER -

References

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