71 citations · 80 across the 7 of their papers we have counts for
5 papers · 1 filter
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…