Spectral isoperimetric inequalities for singular interactions on open arcs
Result description
We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schrodinger operator with an attractive -interaction supported on an open arc with two free endpoints. Under a constraint of fixed length of the arc, we prove that the maximizer is a line segment, the respective spectral isoperimetric inequality being strict. We also show that in the optimization problem for the same spectral quantity, but with the constraint of fixed endpoints, the optimizer is the line segment connecting them. As a consequence of the result for -interaction, we obtain that a line segment is also the maximizer in the optimization problem for the lowest eigenvalue of the Robin Laplacian on a plane with a slit along an open arc of fixed length.
Keywords
delta-interaction on an open arcRobin Laplacian on planes with slitslowest eigenvaluespectral isoperimetric inequalityBirman-Schwinger principle
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Spectral isoperimetric inequalities for singular interactions on open arcs
Original language description
We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schrodinger operator with an attractive -interaction supported on an open arc with two free endpoints. Under a constraint of fixed length of the arc, we prove that the maximizer is a line segment, the respective spectral isoperimetric inequality being strict. We also show that in the optimization problem for the same spectral quantity, but with the constraint of fixed endpoints, the optimizer is the line segment connecting them. As a consequence of the result for -interaction, we obtain that a line segment is also the maximizer in the optimization problem for the lowest eigenvalue of the Robin Laplacian on a plane with a slit along an open arc of fixed length.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applicable Analysis
ISSN
0003-6811
e-ISSN
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Volume of the periodical
98
Issue of the periodical within the volume
8
Country of publishing house
GB - UNITED KINGDOM
Number of pages
11
Pages from-to
1451-1460
UT code for WoS article
000467851300005
EID of the result in the Scopus database
2-s2.0-85041303500
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Applied mathematics
Year of implementation
2019