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

This article is the continuation of our first work on the determination ofthe cases where there is equality in Courant's Nodal Domain theorem in the caseof a Robin boundary condition (with Robin parameter $h$). For the square, ourfirst paper focused on the case where $h$ is large and extended results thatwere obtained by Pleijel, B\'erard--Helffer, for the problem with a Dirichletboundary condition. There, we also obtained some general results about thebehaviour of the nodal structure (for planar domains) under a small deformationof $h$, where $h$ is positive and not close to $0$. In this second paper, weextend results that were obtained by Helffer--Persson-Sundqvist for the Neumannproblem to the case where $h>0$ is small.

Courant-sharp Robin eigenvalues for the square -- the case with small Robin parameter--