Luigi Provenzano

works on

cuboid geometry 1 eigenvalue optimization 1 maxwell eigenvalues 1 shape optimization 1 spectral geometry 1

From the 1 of 4 linked papers with an AI index.

collaborators

4 papers

math.SP2026

Remarks on Weyl-type bounds for Steklov eigenvalues

Luigi Provenzano

We prove that, for $n \geq 3$ , there is no constant $C_{n} > 0$ depending only on $n$ such that the Steklov eigenvalues $σ_{k} (Ω)$ satisfy $|\partialΩ|^{\frac 1{n-1}}σ_k(Ω)\leq C_nk^{\fra…

math.SP2026

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…

math.AP2026

Lane-Emden Problems on Convex Domains of $S^{2}$

Massimo Grossi, Luigi Provenzano, Daniel Raom

We study positive solutions of the Dirichlet problem $- I^ u = u^{p}$ in a uniformly convex domain $I^c ◯ \subset S^{2}$ , $u = 0$ on $\partial I^c ◯ .$ For $p = 1$ , we assume that the right-…

math.AP2025

$H^{2}$ -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 $R^{n}$ are $H^{2}$ regular by adapting a classical argument combined with the Rellich-Pohozaev identity.

Remarks on Weyl-type bounds for Steklov eigenvalues

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

Lane-Emden Problems on Convex Domains of S2

H2-regularity of Steklov eigenfunctions on convex domains via Rellich-Pohozaev identity

Lane-Emden Problems on Convex Domains of $S^{2}$

$H^{2}$ -regularity of Steklov eigenfunctions on convex domains via Rellich-Pohozaev identity