English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider the problem of geometric optimization for the lowest eigenvalueof the two-dimensional Schr\"odinger operator with an attractive$\delta$-interaction supported on an open arc with two free endpoints. Under aconstraint of fixed length of the arc, we prove that the maximizer is a linesegment, the respective spectral isoperimetric inequality being strict. We alsoshow that in the optimization problem for the same spectral quantity, but withthe constraint of fixed endpoints, the optimizer is the line segment connectingthem. As a consequence of the result for $\delta$-interaction, we obtain that aline segment is also the maximizer in the optimization problem for the lowesteigenvalue of the Robin Laplacian on a plane with a slit along an open arc offixed length.

Spectral isoperimetric inequalities for singular interactions on open arcs