Spectral Isoperimetric Inequality for the Delta' -Interaction on a Contour
Result description
We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schrödinger operator with an attractive Delta'-interaction of a fixed strength, the support of which is a C2-smooth contour. Under the constraint of a fixed length of the contour, we prove that the lowest eigenvalue is maximized by the circle. The proof relies on the min-max principle and the method of parallel coordinates.
Keywords
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 Inequality for the Delta' -Interaction on a Contour
Original language description
We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schrödinger operator with an attractive Delta'-interaction of a fixed strength, the support of which is a C2-smooth contour. Under the constraint of a fixed length of the contour, we prove that the lowest eigenvalue is maximized by the circle. The proof relies on the min-max principle and the method of parallel coordinates.
Czech name
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Czech description
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Classification
Type
C - Chapter in a specialist book
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Book/collection name
Springer INdAM Series
ISBN
978-3-030-60452-3
Number of pages of the result
13
Pages from-to
215-227
Number of pages of the book
450
Publisher name
Springer
Place of publication
Cham
UT code for WoS chapter
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Basic information
Result type
C - Chapter in a specialist book
OECD FORD
Pure mathematics
Year of implementation
2021