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

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

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