7 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…
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…
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…
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…
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 ho…
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…