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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we prove that the Extended Courant Property fails to be truefor certain smooth, strictly convex domains with Neumann boundary condition:there exists a linear combination of a second and a first Neumanneigenfunctions, with three nodal domains. For the proof, we revisit adeformation argument of Jerison and Nadirashvili (J. Amer. Math. Soc. 2000,vol. 13). This argument being interesting in itself, we give full details. Inparticular, we carefully control the dependence of the constants on thegeometry of our Lipschitz domains along the deformations.

Level sets of certain Neumann eigenfunctions under deformation of Lipschitz domains. Application to the Extended Courant Property