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Fine bounds for best constants of fractional subcritical Sobolev embeddings and applications to nonlocal PDEs
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Fine bounds for best constants of fractional subcritical Sobolev embeddings and applications to nonlocal PDEs
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Paper
Fine bounds for best constants of fractional subcritical Sobolev embeddings and applications to nonlocal PDEs
2023
Overview
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\\), \\(02s\\) 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.
Publisher
Cornell University Library, arXiv.org
