8 papers
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…
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…
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…