Springer INdAM Series

0542088 - ÚJF 2022 RIV DE eng M - Část monografie knihy
Lotoreichik, Vladimir
Spectral Isoperimetric Inequality for the Delta' -Interaction on a Contour.
Springer INdAM Series. Vol. 42. Cham: Springer, 2021 - (Michelangeli, A.), s. 215-227. ISBN 978-3-030-60452-3
Grant CEP: GA ČR GA17-01706S
Institucionální podpora: RVO:61389005
Klíčová slova: Eigenvalue optimization * lowerst eigenvalue * Min-max principle
Obor OECD: Pure mathematics

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.
Trvalý link: http://hdl.handle.net/11104/0319576