On the location of spectral edges in $\mathbb{Z}$-periodic media
, 2010 Periodic $2$nd order ordinary differential operators on $\R$ are known to have the edges of their spectra to occur only at the spectra of periodic and antiperiodic boundary value problems.
Exner, Pavel +2 more
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Laplacian eigenvalues functionals and metric deformations on compact manifolds [PDF]
, 2007 In this paper, we investigate critical points of the Laplacian's eigenvalues considered as functionals on the space of Riemmannian metrics or a conformal class of metrics on a compact manifold.
Agricola +33 more
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On occurrence of spectral edges for periodic operators inside the Brillouin zone [PDF]
, 2007 The article discusses the following frequently arising question on the spectral structure of periodic operators of mathematical physics (e.g., Schroedinger, Maxwell, waveguide operators, etc.). Is it true that one can obtain the correct spectrum by using
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Isoperimetric inequalities for some integral operators arising in potential theory [PDF]
, 2017 In this paper we review our previous isoperimetric results for the logarithmic potential and Newton potential operators. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they produce a ...
EM Harrell +21 more
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Multiple Aharonov--Bohm eigenvalues: the case of the first eigenvalue on the disk
, 2018 It is known that the first eigenvalue for Aharonov--Bohm operators with half-integer circulation in the unit disk is double if the potential's pole is located at the origin. We prove that in fact it is simple as the pole $a\neq 0$
Abatangelo, Laura
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Hearing the shape of a triangle
, 2013 In 1966 Mark Kac asked the famous question 'Can one hear the shape of a drum?'. While this was later shown to be false in general, it was proved by C. Durso that one can hear the shape of a triangle.
Grieser, Daniel, Maronna, Svenja
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On the torsion function with Robin or Dirichlet boundary conditions
, 2013 For $p\in (1,+\infty)$ and $b \in (0, +\infty]$ the $p$-torsion function with Robin boundary conditions associated to an arbitrary open set $\Om \subset \R^m$ satisfies formally the equation $-\Delta_p =1$ in $\Om$ and $|\nabla u|^{p-2} \frac{\partial u}{
Berg, M. van den, Bucur, D.
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On the number of nodal domains of the 2D isotropic quantum harmonic oscillator -- an extension of results of A. Stern -- [PDF]
, 2014 In the case of the sphere and the square, Antonie Stern (1925) claimed in her PhD thesis the existence of an infinite sequence of eigenvalues whose corresponding eigenspaces contain an eigenfunction with two nodal domains. These two statements were given
Bérard, Pierre, Helffer, Bernard
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Reaction-diffusion problems on time-dependent Riemannian manifolds: stability of periodic solutions
, 2017 We investigate the stability of time-periodic solutions of semilinear parabolic problems with Neumann boundary conditions. Such problems are posed on compact submanifolds evolving periodically in time.
Bandle, Catherine +2 more
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Quantum Ergodicity and Mixing [PDF]
arXiv, 2005 This is an expository article for the Encyclopedia of Mathematical Physics on the subject in the title.
arxiv