7 papers · 1 filter
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…
A degenerating Robin-type traction problem in a periodic domain
Matteo Dalla Riva, Gennady Mishuris, Paolo Musolino
We consider a linearly elastic material with a periodic set of voids. On the boundaries of the voids we set a Robin-type traction condition. Then we investigate the asymptotic beha…
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…
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…
Mapping properties of weakly singular periodic volume potentials in Roumieu classes
Matteo Dalla Riva, Massimo Lanza de Cristoforis, Paolo Musolino
The analysis of the dependence of integral operators on perturbations plays an important role in the study of inverse problems and of perturbed boundary value problems. In this pap…
On vibrating thin membranes with mass concentrated near the boundary: an asymptotic analysis
Matteo Dalla Riva, Luigi Provenzano
We consider the spectral problem \begin{equation*} \left\{\begin{array}{ll} -Δu_{\varepsilon}=λ(\varepsilon)ρ_{\varepsilon}u_{\varepsilon} & {\rm in}\ Ω\\ \frac{\partial u_{\vareps…