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

By Dmitry Jakobson, M. Levitin, Nikolai Nadirashvili, Iosif Polterovich. 2004

47 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1569a2bd185748519d9287fb2020acb35e218c09

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

NUMERICAL SIMULATIONS FOR NODAL DOMAINS AND SPECTRAL MINIMAL PARTITIONS (2010, unknown): “For more details, we refer to [13,17,19].”
On Spectral Minimal Partitions: A Survey (2010, result): “This can be explained by a double covering argument, which is analogous to the argument of isospectrality of Jakobson-Levitin-Nadirashvili-Polterovich [ JNLP ] and Levitin-Parnovski-Polterovich [LPP], see also old papers by B´ erard [Be], Sunada [Su] and the more recent paper by O. Parzanchevski and”
How large can the first eigenvalue be on a surface of genus two (2005, methodology): “However, it was shown in [ JLNP ] that this problem is isospectral to (1.3.3).”