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

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

2004-09-09

arxiv.org/abs/math/0409154v1

Mathematics

Spectral Theory

9 figures

Scientific paper

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.

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