14 papers
The Bilaplacian with Robin boundary conditions
Davide Buoso, James B. Kennedy
We introduce Robin boundary conditions for biharmonic operators, which are a model for elastically supported plates and are closely related to the study of spaces of traces of Sobo…
Interlacing and Friedlander-type inequalities for spectral minimal partitions of metric graphs
Matthias Hofmann, James B. Kennedy
We prove interlacing inequalities between spectral minimal energies of metric graphs built on Dirichlet and standard Laplacian eigenvalues, as recently introduced in [Kennedy et al…
On Pleijel's nodal domain theorem for quantum graphs
Matthias Hofmann, James B. Kennedy, Delio Mugnolo +1
We establish metric graph counterparts of Pleijel's theorem on the asymptotics of the number of nodal domains of the -th eigenfunction(s) of a broad class of operators on…
Asymptotics and estimates for spectral minimal partitions of metric graphs
Matthias Hofmann, James B. Kennedy, Delio Mugnolo +1
We study properties of spectral minimal partitions of metric graphs within the framework recently introduced in [Kennedy et al, Calc. Var. 60 (2021), 61]. We provide sharp lower an…
A theory of spectral partitions of metric graphs
James B. Kennedy, Pavel Kurasov, Corentin Léna +1
We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus…
Disjointness-preserving operators and isospectral Laplacians
Wolfgang Arendt, James B. Kennedy
All the known counterexamples to Kac' famous question "can one hear the shape of a drum", i.e., does isospectrality of two Laplacians on domains imply that the domains are congruen…