| Abstract: |
| It is known that the Faber-Krahn inequality does not hold for Maxwell eigenvalues: regardless of whether a volume or a perimeter constraint is imposed, the ball does not minimize the first eigenvalue. Notably, the first eigenvalue in the ball has multiplicity three.
Motivated by this observation, as well as by a criticality result established by P.D. Lamberti and M. Zaccaron in 2021, we investigate symmetric functions of the first three Maxwell eigenvalues and discuss their potential minimization properties under suitable geometric constraints.
This work is based on a joint collaboration with Pier Domenico Lamberti and Luigi Provenzano. |
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