Comptes Rendus
Mathematical Physics/Calculus of Variations
Shape optimization for the Maxwell equations under weaker regularity of the data
[Dérivée par rapport au domaine dans l'équation de Maxwell sous des hypothèses de plus faible régularité des données]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1225-1230.

On considère un problème d'optimisation de forme dans le cadre des équations de Maxwell avec une condition de bord dissipative. On établit un résultat de dérivabilité par rapport au domaine dans le cas de faible régularité. Au détour de cette preuve, on établit la régularité « cachée » des traces du champ éléctrique et magnétique sur le bord du domaine.

We consider a shape optimization problem for Maxwell's equations with a strictly dissipative boundary condition. In order to characterize the shape derivative as a solution to a boundary value problem, sharp regularity of the boundary traces is critical. This Note establishes the Fréchet differentiability of a shape functional.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.10.021

John Cagnol 1 ; Matthias Eller 2

1 École Centrale Paris, laboratoire MAS, grande voie des vignes, 92295 Chatenay-Malabry cedex, France
2 Georgetown University, Dept. of Mathematics, Washington, DC 20057, USA
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     title = {Shape optimization for the {Maxwell} equations under weaker regularity of the data},
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John Cagnol; Matthias Eller. Shape optimization for the Maxwell equations under weaker regularity of the data. Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1225-1230. doi : 10.1016/j.crma.2010.10.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.021/

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