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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We establish fine bounds for best constants of the fractional subcriticalSobolev embeddings \begin{align*} W_{0}^{s,p}\left(\Omega\right)\hookrightarrowL^{q}\left(\Omega\right), \end{align*} where $N\geq1$, $0<s<1$, $p=1,2$, $1\leqq<p_{s}^{\ast}=\frac{Np}{N-sp}$ and $\Omega\subset\mathbb{R}^{N}$ is a boundedsmooth domain or the whole space $\mathbb{R}^{N}$. Our results cover theborderline case $p=1$, the Hilbert case $p=2$, $N>2s$ and the so-called Sobolevlimiting case $N=1$, $s=\frac{1}{2}$ and $p=2$, where a sharp asymptoticestimate is given by means of a limiting procedure. We apply the obtainedresults to prove existence and non-existence of solutions for a wide class ofnonlocal partial differential equations.

Fine bounds for best constants of fractional subcritical Sobolev embeddings and applications to nonlocal PDEs