22 citations · 102 across the 33 of their papers we have counts for
37 papers
Corrigendum to "Ramification of multiple eigenvalues for the Dirichlet-Laplacian in perforated domains" published in Journal of Functional Analysis 283 (2022) 109718
Laura Abatangelo, Corentin Léna, Paolo Musolino
We fix the proof of Theorem 1.17 in the quoted reference, which does not in general gives the correct coefficients in the asymptotic behavior of eigenvalues for the Dirichlet Lapla…
Shape differentials and sensitivity of the heat equation
Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino
We consider Dirichlet and Neumann problems for the heat equation in a domain containing an interior hole. The domain has a fixed outer boundary and a variable inner boundary determ…
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…
Regularity properties of certain convolution operators in Hölder spaces
Matteo Dalla Riva, Massimo Lanza de Cristoforis, Paolo Musolino
The aim of this paper is to prove a theorem of C.~Miranda on the Hölder regularity of convolution operators acting on the boundary of an open set in the limiting case in which the…
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…
Dirichlet problem on perturbed conical domains via converging generalized power series
Martin Costabel, Matteo Dalla Riva, Monique Dauge +1
We consider the Poisson equation with homogeneous Dirichlet conditions in a family of domains in indexed by a small parameter . The domains depend on only within a b…
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…
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…
Asymptotic behavior of generalized capacities with applications to eigenvalue perturbations: the higher dimensional case
Laura Abatangelo, Corentin Léna, Paolo Musolino
We provide a full series expansion of a generalization of the so-called -capacity related to the Dirichlet-Laplacian in dimension three and higher, extending previous results of…
Asymptotic analysis a perturbed Robin problem in a planar domain
Paolo Musolino, Martin Dutko, Gennady Mishuris
We consider a perforated domain of with a small hole of size and we study the behavior of the solution of a mixed Neumann-Robin problem in as the s…
Existence results for a nonlinear nonautonomus transmission problem via domain perturbation
Matteo Dalla Riva, Riccardo Molinarolo, Paolo Musolino
In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equatio…
Local uniqueness of the solutions for a singularly perturbed nonlinear nonautonomous transmission problem
Matteo Dalla Riva, Riccardo Molinarolo, Paolo Musolino
We consider the Laplace equation in a domain of , , with a small inclusion of size . On the boundary of the inclusion we define a nonlinear nonautonomous t…
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…
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…
Integral equation method for a Robin-type traction problem in a periodic domain
Matteo Dalla Riva, Gennady Mishuris, Paolo Musolino
In this note, we consider a Robin-type traction problem for a linearly elastic body occupying an infinite periodically perforated domain. After proving the uniqueness of the soluti…
Interaction of scales for a singularly perturbed degenerating nonlinear Robin problem
Paolo Musolino, Gennady Mishuris
We study the asymptotic behavior of the solutions of a boundary value problem for the Laplace equation in a perforated domain in , , with a (nonlinear) Robin…
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…
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…
Ramification of multiple eigenvalues for the Dirichlet-Laplacian in perforated domains
Laura Abatangelo, Corentin Léna, Paolo Musolino
Taking advantage from the so-called "Lemma on small eigenvalues" by Colin de Verdière, we study ramification for multiple eigenvalues of the Dirichlet Laplacian in bounded perforat…
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…
Asymptotic behavior of -capacities and singular perturbations for the Dirichlet-Laplacian
Laura Abatangelo, Virginie Bonnaillie-Noël, Corentin Léna +1
In this paper we study the asymptotic behavior of -capacities of small sets and its application to the analysis of the eigenvalues of the Dirichlet-Laplacian on a bounded planar…
A mixed problem for the Laplace operator in a domain with moderately close holes
Matteo Dalla Riva, Paolo Musolino
We investigate the behavior of the solution of a mixed problem in a domain with two moderately close holes. We introduce a positive parameter and we define a perforated domain…