Boundary regularity for Maxwell's equations with applications to shape optimization

John Cagnol (1) , Matthias Eller (2)

1 Ecole Centrale Paris
2 GU - Georgetown University [Washington]

The dynamic Maxwell equations with a strictly dissipative boundary condition is considered. Sharp trace regularity for the electric and the magnetic field are established for both: weak and differ-entiable solutions. As an application a shape optimization problem for Maxwell's equations is considered. In order to characterize the shape derivative as a solution to a boundary value problem, the aforementioned sharp regularity of the boundary traces is critical.

Mots clés: Shape optimization; Maxwell's equations; Boundary value problems

Domaines: Mathématiques [math]

John Cagnol, Matthias Eller. Boundary regularity for Maxwell's equations with applications to shape optimization. Journal of Differential Equations, 2011, 250 (2), pp.1114-1136. ⟨10.1016/j.jde.2010.08.004⟩. ⟨hal-01570315⟩