Luigi Provenzano · wovepaper

activity

20122026

most citedA maximum principle in spectral optimization problems for elliptic operators subject to mass density perturbations

12 citations · 16 across the 7 of their papers we have counts for

collaborators

9 papers

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…

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

Pier Domenico Lamberti, Luigi Provenzano, Rebecca Sempio

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 th…

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

Massimo Grossi, Luigi Provenzano, Daniel Raom

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

$H^{2}$ -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.

math.FA2019★ 4 cited

On Trace Theorems for Sobolev Spaces

Pier Domenico Lamberti, Luigi Provenzano

We survey a few trace theorems for Sobolev spaces on $N$ -dimensional Euclidean domains. We include known results on linear subspaces, in particular hyperspaces, and smooth boundari…

On the explicit representation of the trace space $H^{\frac{3}{2}}$ and of the solutions to biharmonic Dirichlet problems on Lipschitz domains via multi-parameter Steklov problems

Pier Domenico Lamberti, Luigi Provenzano

We consider the problem of describing the traces of functions in $H^{2} (Ω)$ on the boundary of a Lipschitz domain $Ω$ of $R^{N}$ , $N \geq 2$ . We provide a definition of those sp…

Neumann to Steklov eigenvalues: asymptotic and monotonicity results

Pier Domenico Lamberti, Luigi Provenzano

We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of mass concentration at the boundary of a ball. We discuss the asymptotic…

Viewing the Steklov eigenvalues of the Laplace operator as critical Neumann eigenvalues

Pier Domenico Lamberti, Luigi Provenzano

We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of boundary mass concentration. We discuss the asymptotic behavior of the N…

math.SP2012★ 12 cited

A maximum principle in spectral optimization problems for elliptic operators subject to mass density perturbations

Pier Domenico Lamberti, Luigi Provenzano

We consider eigenvalue problems for general elliptic operators of arbitrary order subject to homogeneous boundary conditions on open subsets of the euclidean N-dimensional space. W…