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arXiv · 2305.09486

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

Daniele Cassani·Lele Du
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Abstract

We establish fine bounds for best constants of the fractional subcritical Sobolev embeddings \begin{align*} W_{0}^{s,p}\left(\Omega\right)\hookrightarrow L^{q}\left(\Omega\right), \end{align*} where $N\geq1$, $0 2s$ and the so-called Sobolev limiting case $N=1$, $s=\frac{1}{2}$ and $p=2$, where a sharp asymptotic estimate is given by means of a limiting procedure. We apply the obtained results to prove existence and non-existence of solutions for a wide class of nonlocal partial differential equations.

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Daniele Cassani, Lele Du. 2023-05-16. Fine bounds for best constants of fractional subcritical Sobolev embeddings and applications to nonlocal PDEs. https://arxiv.org/abs/2305.09486

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