5 papers
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…
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 $- Î_αu= Vu…