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

Chikouche, Wided; Nicaise, Serge

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

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

Classification : 35A20, 35Q60, 78A25

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