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Optimal embedding results for fractional Sobolev spaces

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arxiv 2411.12245 v1 pith:ZV4KMETS submitted 2024-11-19 math.AP

Serena Dipierro , Edoardo Proietti Lippi , Caterina Sportelli , Enrico Valdinoci This is my paper
classification math.AP
keywords omegaresultsspacesembeddingboundaryboundedclassicalcontinuous
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abstract

This paper deals with the fractional Sobolev spaces $W^{s, p}(\Omega)$, with $s\in (0, 1]$ and $p\in[1,+\infty]$. Here, we use the interpolation results in [4] to provide suitable conditions on the exponents $s$ and $p$ so that the spaces $W^{s, p}(\Omega)$ realize a continuous embedding when either $\Omega=\mathbb R^N$ or $\Omega$ is any open and bounded domain with Lipschitz boundary. Our results enhance the classical continuous embedding and, when $\Omega$ is any open bounded domain with Lipschitz boundary, we also improve the classical compact embeddings. All the results stated here are proved to be optimal. Also, our strategy does not require the use of Besov or other interpolation spaces.

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Cited by 3 Pith papers

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