Spectral isoperimetric inequalities for singular interactions on open arcs

0505085 - ÚJF 2020 RIV GB eng J - Journal Article
Lotoreichik, Vladimir
Spectral isoperimetric inequalities for singular interactions on open arcs.
Applicable Analysis. Roč. 98, č. 8 (2019), s. 1451-1460. ISSN 0003-6811. E-ISSN 1563-504X
R&D Projects: GA ČR(CZ) GA14-06818S
Institutional support: RVO:61389005
Keywords : delta-interaction on an open arc * Robin Laplacian on planes with slits * lowest eigenvalue * spectral isoperimetric inequality * Birman-Schwinger principle
OECD category: Applied mathematics
Impact factor: 1.107, year: 2019
Method of publishing: Limited access
https://doi.org/10.1080/00036811.2018.1430778

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.
Permanent Link: http://hdl.handle.net/11104/0296603