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Extensions self-adjointes et anti-symétriques du laplacien, avec condition à la frontière de type Robin singulière. / Nazarov, S.A.; Popoff, N.

In: Comptes Rendus Mathematique, Vol. 356, No. 9, 09.2018, p. 927-932.

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

Harvard

Nazarov, SA & Popoff, N 2018, 'Extensions self-adjointes et anti-symétriques du laplacien, avec condition à la frontière de type Robin singulière', Comptes Rendus Mathematique, vol. 356, no. 9, pp. 927-932. https://doi.org/10.1016/j.crma.2018.07.001

APA

Nazarov, S. A., & Popoff, N. (2018). Extensions self-adjointes et anti-symétriques du laplacien, avec condition à la frontière de type Robin singulière. Comptes Rendus Mathematique, 356(9), 927-932. https://doi.org/10.1016/j.crma.2018.07.001

Vancouver

Nazarov SA, Popoff N. Extensions self-adjointes et anti-symétriques du laplacien, avec condition à la frontière de type Robin singulière. Comptes Rendus Mathematique. 2018 Sep;356(9):927-932. https://doi.org/10.1016/j.crma.2018.07.001

Author

Nazarov, S.A. ; Popoff, N. / Extensions self-adjointes et anti-symétriques du laplacien, avec condition à la frontière de type Robin singulière. In: Comptes Rendus Mathematique. 2018 ; Vol. 356, No. 9. pp. 927-932.

BibTeX

@article{cc0ce1cfe9974f319618c35554ddd5b8,
title = "Extensions self-adjointes et anti-sym{\'e}triques du laplacien, avec condition {\`a} la fronti{\`e}re de type Robin singuli{\`e}re",
abstract = "We study the Laplacian in a bounded domain, with a varying Robin boundary condition singular at one point. The associated quadratic form is not semi-bounded from below, and the corresponding Laplacian is not self-adjoint, it has a residual spectrum covering the whole complex plane. We describe its self-adjoint extensions and exhibit a physically relevant skew-symmetric one. We approximate the boundary condition, giving rise to a family of self-adjoint operators, and we describe its spectrum by the method of matched asymptotic expansions. A part of the spectrum acquires a strange behavior when the small perturbation parameter ε>0 tends to zero, namely it becomes almost periodic in the logarithmic scale |ln⁡ε|, and in this way “wanders” along the real axis at a speed O(ε −1). ",
author = "S.A. Nazarov and N. Popoff",
note = "Funding Information: This work is supported by grant 17-11-01003 of the Russian Science Foundation . It is also supported by the Chair BOLIDE funded by the IDEX Bordeaux and by the project PEPS JC 2017.",
year = "2018",
month = sep,
doi = "10.1016/j.crma.2018.07.001",
language = "французский",
volume = "356",
pages = "927--932",
journal = "Comptes Rendus Mathematique",
issn = "1631-073X",
publisher = "Elsevier",
number = "9",

}

RIS

TY - JOUR

T1 - Extensions self-adjointes et anti-symétriques du laplacien, avec condition à la frontière de type Robin singulière

AU - Nazarov, S.A.

AU - Popoff, N.

N1 - Funding Information: This work is supported by grant 17-11-01003 of the Russian Science Foundation . It is also supported by the Chair BOLIDE funded by the IDEX Bordeaux and by the project PEPS JC 2017.

PY - 2018/9

Y1 - 2018/9

N2 - We study the Laplacian in a bounded domain, with a varying Robin boundary condition singular at one point. The associated quadratic form is not semi-bounded from below, and the corresponding Laplacian is not self-adjoint, it has a residual spectrum covering the whole complex plane. We describe its self-adjoint extensions and exhibit a physically relevant skew-symmetric one. We approximate the boundary condition, giving rise to a family of self-adjoint operators, and we describe its spectrum by the method of matched asymptotic expansions. A part of the spectrum acquires a strange behavior when the small perturbation parameter ε>0 tends to zero, namely it becomes almost periodic in the logarithmic scale |ln⁡ε|, and in this way “wanders” along the real axis at a speed O(ε −1).

AB - We study the Laplacian in a bounded domain, with a varying Robin boundary condition singular at one point. The associated quadratic form is not semi-bounded from below, and the corresponding Laplacian is not self-adjoint, it has a residual spectrum covering the whole complex plane. We describe its self-adjoint extensions and exhibit a physically relevant skew-symmetric one. We approximate the boundary condition, giving rise to a family of self-adjoint operators, and we describe its spectrum by the method of matched asymptotic expansions. A part of the spectrum acquires a strange behavior when the small perturbation parameter ε>0 tends to zero, namely it becomes almost periodic in the logarithmic scale |ln⁡ε|, and in this way “wanders” along the real axis at a speed O(ε −1).

UR - http://www.scopus.com/inward/record.url?scp=85049871924&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2018.07.001

DO - 10.1016/j.crma.2018.07.001

M3 - статья

VL - 356

SP - 927

EP - 932

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 9

ER -

ID: 35209824