On the principal eigenvalue of a Robin problem with a large parameter
By M. Levitin, L. Parnovski. 2004
109 citations recorded by the source corpus.
We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two‐sided estimates for this term in a variety of situations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ed7a7f76ecef5a7b2081f1815e9be13e93cc34af
How researchers see this paper
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In Applied Mathematics
- Jussi Behrndt
- H. D. de Snoo
- S. Hassi
- Konstantin Pankrashkin
- Nicolas Popoff
- James B. Kennedy
- Daniel Daners
- Dorin Bucur
In Computational Theory and Mathematics
- Konstantin Pankrashkin
- Nicolas Popoff
- S. Hassi
- H. D. de Snoo
- Jussi Behrndt
- James B. Kennedy
- Daniel Daners
- Dorin Bucur
In Mathematical Physics
- H. D. de Snoo
- S. Hassi
- Jussi Behrndt
- Nicolas Popoff
- Konstantin Pankrashkin
- James B. Kennedy
- Daniel Daners
- Matthias Langer
Citations in the corpus
- On the asymptotic behaviour of the eigenvalues of a Robin problem (2009, background): “This problem has received considerable attention in the last few years; see for example [1, 4, 5, 6, 8, 9 , 10] and the references therein.”
- An effective Hamiltonian for the eigenvalue asymptotics of the Robin Laplacian with a large parameter (2015, background): “More detailed asymptotic expansions for some specific non-smooth domains were considered in [18,27,32].”
- Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities (2008, unknown): “We refer, for instance, to [2], [3], [4], [10], [12], [13], [14], [15], [17], [25], [26], [28], [29], [35], [37], [40], [52], and the literature cited therein.”
- Boundary Value Problems, Weyl Functions, and Differential Operators (2020, background): “Particular attention has been paid to the spectral properties of realizations with local and nonlocal Robin boundary conditions in [41, 106, 179, 180, 226, 325, 361, 413, 543, 628, 629, 665].”