Spectral problems with mixed Dirichlet-Neumann boundary conditions: Isospectrality and beyond

Dmitry Jakobson, Michael Levitin, Nikolai Nadirashvili, Iosif Polterovich

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

Consider a bounded domain with the Dirichlet condition on a part of the boundary and the Neumann condition on its complement. Does the spectrum of the Laplacian determine uniquely which condition is imposed on which part? We present some results, conjectures and problems related to this variation on the isospectral theme. © 2005 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)141-155
Number of pages15
JournalJournal of Computational and Applied Mathematics
Volume194
Issue number1 SPEC. ISS.
DOIs
Publication statusPublished - 15 Sep 2006

Keywords

  • Isospectrality
  • Laplacian
  • Mixed Dirichlet-Neumann problem
  • Zaremba problem

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