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

Chikouche, Wided; Nicaise, Serge

Chikouche, Wided ; Nicaise, Serge

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 3, pp. 455-482.

Résumé

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.

MR 2466437 | Zbl 1183.35260

Classification : 35A20, 35Q60, 78A25

@article{ASNSP_2008_5_7_3_455_0,
     author = {Chikouche, Wided and Nicaise, Serge},
     title = {Singularities of Maxwell's system in non-hilbertian Sobolev spaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {455--482},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 7},
     number = {3},
     year = {2008},
     zbl = {1183.35260},
     mrnumber = {2466437},
     language = {en},
     url = {archive.numdam.org/item/ASNSP_2008_5_7_3_455_0/}
}

Chikouche, Wided; Nicaise, Serge. Singularities of Maxwell's system in non-hilbertian Sobolev spaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 3, pp. 455-482. http://archive.numdam.org/item/ASNSP_2008_5_7_3_455_0/

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