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Spectral isoperimetric inequalities for singular interactions on open arcs
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SYSNO ASEP 0505085 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Spectral isoperimetric inequalities for singular interactions on open arcs Author(s) Lotoreichik, Vladimir (UJF-V) ORCID, SAI Number of authors 1 Source Title Applicable Analysis. - : Taylor & Francis - ISSN 0003-6811
Roč. 98, č. 8 (2019), s. 1451-1460Number of pages 11 s. Publication form Print - P Language eng - English Country GB - United Kingdom Keywords delta-interaction on an open arc ; Robin Laplacian on planes with slits ; lowest eigenvalue ; spectral isoperimetric inequality ; Birman-Schwinger principle Subject RIV BA - General Mathematics OECD category Applied mathematics R&D Projects GA14-06818S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support UJF-V - RVO:61389005 UT WOS 000467851300005 EID SCOPUS 85041303500 DOI 10.1080/00036811.2018.1430778 Annotation 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2020 Electronic address https://doi.org/10.1080/00036811.2018.1430778
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