71 citations · 80 across the 7 of their papers we have counts for
8 papers
Positivity properties of the Dirichlet-to-Neumann operator on graphs
Daniel Daners, Jochen Glück, James B. Kennedy
We explore positivity properties of the semigroup generated by the negative of the Dirichlet-to-Neumann operator with real potential , defined on a subset of the vertices of a q…
On the hot spots conjecture in higher dimensions
James B. Kennedy, Jonathan Rohleder
We prove a strong form of the hot spots conjecture for a class of domains in which are a natural generalization of the lip domains of Atar and Burdzy [J. Amer. Math.…
Geometric spectral theory of quantum graphs
James Kennedy
These are lecture notes from a course given at the summer school "Heat kernels and spectral geometry: from manifolds to graphs" in Bregenz, Austria, 2022. They are designed to be a…
A toy Neumann analogue of the nodal line conjecture
J. B. Kennedy
We introduce an analogue of Payne's nodal line conjecture, which asserts that the nodal (zero) set of any eigenfunction associated with the second eigenvalue of the Dirichlet Lapla…
Analytical aspects of isospectral drums
W. Arendt, A. F. M. ter Elst, J. B. Kennedy
We reexamine the proofs of isospectrality of the counterexample domains to Kac' question `Can one hear the shape of a drum?' from an analytical viewpoint. We reformulate isospectra…
The Dirichlet-to-Neumann operator via hidden compactness
W. Arendt, A. F. M. ter Elst, J. B. Kennedy +1
We show that to each symmetric elliptic operator of the form \[ \mathcal{A} = - \sum \partial_k \, a_{kl} \, \partial_l + c \] on a bounded Lipschitz domain …
Closed nodal surfaces for simply connected domains in higher dimensions
J. B. Kennedy
We give an example of a domain in dimension , homeomorphic to a ball and with analytic boundary, for which the second eigenvalue of the Dirichlet Laplacian has an eigenfu…
Some remarks on the isoperimetric problem for the higher eigenvalues of the Robin and Wentzell Laplacians
J. B. Kennedy
We consider the problem of minimising the th eigenvalue, , of the (-)Laplacian with Robin boundary conditions with respect to all domains in of given…