From the 1 of 7 linked papers with an AI index.
7 papers
On a shape optimisation problem for Maxwell's eigenvalues on cuboids
Pier Domenico Lamberti, Luigi Provenzano, Rebecca Sempio
The paper studies how to shape a rectangular box (cuboid) to minimize certain combinations of the first three Maxwell eigenvalues under fixed volume and perimeter, showing that the…
Asymptotic behavior and spectral distortion for biharmonic Steklov problems on thin domains
Bauyrzhan Derbissaly, Pier Domenico Lamberti
In this paper, we investigate the asymptotic behavior of the eigenvalues and eigenfunctions of a biharmonic Steklov problem defined on a thin domain in the dimensional Euclidea…
The nonlinear Steklov problem in outward cuspidal domains
Pier Domenico Lamberti, Alexander Ukhlov
In this article, we consider the nonlinear Steklov eigenvalue problem in outward cuspidal domains. Using the compactness of the weighted trace embedding we obtain the variational c…
Steklov vs. Steklov: A Fourth-Order Affair Related to the Babuška Paradox
Francesco Ferraresso, Pier Domenico Lamberti
We discuss two fourth-order Steklov problems and highlight a BabuÅ¡ka paradox appearing in their approximations on convex domains via sequences of convex polygons. To do so, we pro…
Shape sensitivity analysis of Neumann-Poincaré eigenvalues
Matteo Dalla Riva, Pier Domenico Lamberti, Paolo Luzzini +1
This paper concerns the eigenvalues of the Neumann-Poincaré operator, a boundary integral operator associated with the harmonic double-layer potential. Specifically, we examine ho…
-regularity of Steklov eigenfunctions on convex domains via Rellich-Pohozaev identity
Pier Domenico Lamberti, Luigi Provenzano
We prove that the Steklov eigenfunctions on convex domains of are regular by adapting a classical argument combined with the Rellich-Pohozaev identity.