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math.AP2013
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…
math.AP2013★ 71 cited
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 …