Boundary regularity for Maxwell's equations with applications to shape optimization |
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Authors: | John Cagnol |
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Institution: | a Ecole Centrale Paris, Applied Mathematics and Systems Department, Grande Voie des Vignes, 92295 Chatenay-Malabry, France b Department of Mathematics, Georgetown University, Washington, DC 20057, United States |
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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 differentiable 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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Keywords: | Maxwell's equations Boundary value problems Shape optimization |
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