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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider Dirichlet Laplacians on straight strips in R^2 or layers in R^3with a weak local deformation. First we generalize a result of Bulla et al. tothe three-dimensional situation showing that weakly coupled bound states existif the volume change induced by the deformation is positive; we also derive theleading order of the weak-coupling asymptotics. With the knowledge of theeigenvalue analytic properties, we demonstrate then an alternative method whichmakes it possible to evaluate the next term in the asymptotic expansion forboth the strips and layers. It gives, in particular, a criterion for thebound-state existence in the critical case when the added volume is zero.Comment: LaTeX2e, 25 pages; to appear in Annales H. Poincar

Bound States in Weakly Deformed Strips and Layers