14 papers · 1 filter
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…
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…
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…
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 in…
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…
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…