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

Dmitry Jakobson; Michael Levitin; Nikolai Nadirashvili; Iosif Polterovich

doi:10.1016/j.cam.2005.06.019

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

Dmitry Jakobson
, Michael Levitin
, Nikolai Nadirashvili
, Iosif Polterovich

Research output: Contribution to journal › Article › peer-review

28 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 language	English
Pages (from-to)	141-155
Number of pages	15
Journal	Journal of Computational and Applied Mathematics
Volume	194
Issue number	1 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.cam.2005.06.019
Publication status	Published - 15 Sept 2006

Keywords

Isospectrality
Laplacian
Mixed Dirichlet-Neumann problem
Zaremba problem

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10.1016/j.cam.2005.06.019

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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. {\textcopyright} 2005 Elsevier B.V. All rights reserved.",

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AU - Jakobson, Dmitry

AU - Levitin, Michael

AU - Nadirashvili, Nikolai

AU - Polterovich, Iosif

PY - 2006/9/15

Y1 - 2006/9/15

N2 - 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.

AB - 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.

KW - Isospectrality

KW - Laplacian

KW - Mixed Dirichlet-Neumann problem

KW - Zaremba problem

U2 - 10.1016/j.cam.2005.06.019

DO - 10.1016/j.cam.2005.06.019

M3 - Article

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VL - 194

SP - 141

EP - 155

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1 SPEC. ISS.

ER -

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

Abstract

Keywords

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