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Published December 1991 | public
Journal Article

The essential spectrum of Neumann Laplacians on some bounded singular domains

Abstract

In the present paper we consider Neumann Laplacians on singular domains of the type "rooms and passages" or "combs" and we show that, in typical situations, the essential spectrum can be determined from the geometric data. Moreover, given an arbitrary closed subset S of the non-negative reals, we construct domains Ω = Ω(S) such that the essential spectrum of the Neumann Laplacian on Ω is just this set S.

Additional Information

© 1991 Elsevier Inc. Received 2 August 1990. Research supported by Deutsche Forschungsgemeinschaft and by USNSF under Grant DMS-8807816.

Additional details

Created:
August 20, 2023
Modified:
October 17, 2023