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

The paper provides two versions of nonlocal Poincar\'e-type inequalities forintegral operators with a convolution-type structure and functions satisfying azero-Dirichlet like condition. The inequalities extend existing results to alarge class of nonhomogeneous kernels with supports that can varydiscontinuously and need not contain a common set throughout the domain. Themeasure of the supports may even vanish allowing the zero-Dirichlet conditionto be imposed on only a lower-dimensional manifold, with or without boundary.The conditions may be imposed on sets with co-dimension larger than one or evenat just a single point. This appears to currently be the first such results ina nonlocal setting with integrable kernels. The arguments used are direct, andexamples are provided demonstrating the explicit dependence of bounds for thePoincar\'{e} constant upon structural parameters of the kernel and domain.

Nonlocal Poincar\'{e} Inequalities for Integral Operators with Integrable Nonhomogeneous Kernels