4 citations · 9 across the 18 of their papers we have counts for
20 papers
Grushin spherical harmonics in non-degenerate dimension one
Roberto Bramati, Paolo Luzzini
The Grushin Laplacian is a degenerate elliptic operator in that degenerates on . We explicitly compute the Gr…
Shape sensitivity analysis of the heat equation and the Dirichlet-to-Neumann map
Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino
We study a Dirichlet problem for the heat equation in a domain containing an interior hole. The domain has a fixed outer boundary and a variable inner boundary determined by a diff…
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 how…
Periodic layer potentials and domain perturbations
Roberto Bramati, Matteo Dalla Riva, Paolo Luzzini +1
In this paper, we review the construction of periodic fundamental solutions and periodic layer potentials for various differential operators. Specifically, we focus on the Laplace…
On solutions to a class of degenerate equations with the Grushin operator
Laura Abatangelo, Alberto Ferrero, Paolo Luzzini
The Grushin Laplacian is a degenerate elliptic operator in that degenerates on . We consider weak solutions of in…
Shape perturbation of a nonlinear mixed problem for the heat equation
Matteo Dalla Riva, Paolo Luzzini, Riccardo Molinarolo +1
We consider the heat equation in a domain that has a hole in its interior. We impose a Neumann condition on the exterior boundary and a nonlinear Robin condition on the boundary of…
Permittivity optimization for Maxwell's eigenvalues
Pier Domenico Lamberti, Paolo Luzzini, Michele Zaccaron
We formulate an optimization problem for the dependence of the eigenvalues of Maxwell's equations in a cavity upon variation of the electric permittivity and we prove a correspondi…
Multi-parameter perturbations for the space-periodic heat equation
Matteo Dalla Riva, Paolo Luzzini, Riccardo Molinarolo +1
This paper is divided into three parts. The first part focuses on periodic layer heat potentials, demonstrating their smooth dependence on regular perturbations of the support of i…
Dependence of the layer heat potentials upon support perturbations
Matteo Dalla Riva, Paolo Luzzini
We prove that the integral operators associated with the layer heat potentials depend smoothly upon a parametrization of the support of integration. The analysis is carried out in…
Singular behavior for a multi-parameter periodic Dirichlet problem
Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino
We consider a Dirichlet problem for the Poisson equation in a periodically perforated domain. The geometry of the domain is controlled by two parameters: a real number propor…
The Functional Analytic Approach for quasi-periodic boundary value problems for the Helmholtz equation
Roberto Bramati, Matteo Dalla Riva, Paolo Luzzini +1
We lay down the preliminary work to apply the Functional Analytic Approach to quasi-periodic boundary value problems for the Helmholtz equation. This consists in introducing a quas…
Semiclassical estimates for eigenvalue means of Laplacians on spheres
Davide Buoso, Paolo Luzzini, Luigi Provenzano +1
We compute three-term semiclassical asymptotic expansions of counting functions and Riesz-means of the eigenvalues of the Laplacian on spheres and hemispheres, for both Dirichlet a…
Shape analyticity and singular perturbations for layer potential operators
Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino
We study the effect of regular and singular domain perturbations on layer potential operators for the Laplace equation. First, we consider layer potentials supported on a diffeomor…
The first Grushin eigenvalue on cartesian product domains
Paolo Luzzini, Luigi Provenzano, Joachim Stubbe
In this paper we consider the first eigenvalue of the Grushin operator with Dirichlet boundary conditions on a bounded domain of $\mat…
A perturbation result for a Neumann problem in a periodic domain
Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino
We consider a Neumann problem for the Laplace equation in a periodic domain. We prove that the solution depends real analytically on the shape of the domain, on the periodicity par…
A few results on permittivity variations in electromagnetic cavities
Paolo Luzzini, Michele Zaccaron
We study the eigenvalues of time-harmonic Maxwell's equations in a cavity upon changes in the electric permittivity of the medium. We prove that all the eigenvalues,…
Multi-parameter analysis of the obstacle scattering problem
Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino
We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an ext…
A mapping property of the heat volume potential
Paolo Luzzini
We consider the volume potential associated with the heat operator and we prove a mapping property in the space of distributions which are the time derivative of Hölder continuous…
On the spectral asymptotics for the buckling problem
Davide Buoso, Paolo Luzzini, Luigi Provenzano +1
We provide a direct proof of Weyl's law for the buckling eigenvalues of the biharmonic operator on a wide class of domains of including bounded Lipschitz domains. The…
Shape perturbation of Grushin eigenvalues
Pier Domenico Lamberti, Paolo Luzzini, Paolo Musolino
We consider the spectral problem for the Grushin Laplacian subject to homogeneous Dirichlet boundary conditions on a bounded open subset of . We prove that the symmet…