On a shape optimisation problem for Maxwell's eigenvalues on cuboids

2026/07/29 by Pier Domenico Lamberti, Luigi Provenzano, Rebecca Sempio
Mathematics · #math.SP #msc:35P15 #msc:35Q61 #msc:49K20

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arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

We consider an optimisation problem for the elementary symmetric functions of the first three Maxwell's eigenvalues on cuboids under volume and perimeter constraint, and we show that the cube is a local minimiser. More precisely, it is the unique minimiser in an explicit cone of cuboids. The result gives a model case for the local optimisation of Maxwell's eigenvalues. On the other hand we show that such local extremality phenomena cannot be expected outside rigid geometric classes.

Citations

• A note on the Maxwell's eigenvalues on thin sets
• Shape perturbation of Grushin eigenvalues
• Shape sensitivity analysis for electromagnetic cavities
• Eigenvalue problems in inverse electromagnetic scattering theory
• On the Maxwell Constants in 3D
• Eigenvalues of poly-harmonic operators on variable domains

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