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 paper is devoted to an extension of rigidity results for nonlineardifferential equations, based on carr{\'e} du champ methods, in theone-dimensional periodic case. The main result is an interpolation inequalitywith non-trivial explicit estimates of the constants in W1,p(S1) with p $\ge$2. Mostly for numerical reasons, we relate our estimates with issues concerningperiodic dynamical systems. Our interpolation inequalities have a dualformulation in terms of generalized spectral estimates of Keller-Lieb-Thirringtype, where the differential operator is now a p-Laplacian type operator. It isremarkable that the carr{\'e} du champ method adapts to such a nonlinearframework, but significant changes have to be done and, for instance, theunderlying parabolic equation has a nonlocal term whenever p$\ne$2.

Interpolation inequalities in W1,p(S1) and carr{\'e} du champ methods