4 papers
Geometric spectral properties of electromagnetic waveguides
Philippe Briet, Maxence Cassier, Thomas Ourmières-Bonafos +1
Consider a reference homogeneous and isotropic electromagnetic waveguide with a simply connected cross-section embedded in a perfect conductor. In this setting, when the waveguide…
Shape Derivatives of the Eigenvalues of the De Rham Complex for Lipschitz Deformations and Variable Coefficients: Part II
Pier Domenico Lamberti, Dirk Pauly, Michele Zaccaron
In this second part of our series of papers, we develop an abstract framework suitable for de Rham complexes that depend on a parameter belonging to an arbitrary Banach space. Our…
Shape Derivatives of the Eigenvalues of the De Rham Complex for Lipschitz Deformations and Variable Coefficients: Part I
Pier Domenico Lamberti, Dirk Pauly, Michele Zaccaron
We study eigenvalue problems for the de Rham complex on varying three dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed bou…
A note on the failure of the Faber-Krahn inequality for the vector Laplacian
David Krejcirik, Pier Domenico Lamberti, Michele Zaccaron
We consider a natural eigenvalue problem for the vector Laplacian related to stationary Maxwell's equations in a cavity and we prove that an analog of the celebrated Faber-Krahn in…