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

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...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2006-09, Vol.194 (1), p.141-155
Main Authors: Jakobson, Dmitry, Levitin, Michael, Nadirashvili, Nikolai, Polterovich, Iosif
Format: Article
Language:English
Subjects:
Exact sciences and technology
Global analysis, analysis on manifolds
Isospectrality
Laplacian
Mathematical analysis
Mathematics
Mixed Dirichlet–Neumann problem
Partial differential equations
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Zaremba problem
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2005.06.019