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• W2070851924 abstract "We collect and extend results on the limit of $sigma^{1-k}(1-sigma)^k |v|_{l+sigma,p,Omega}^p$ as $sigma$ tends to $0^+$ or $1^-$, where $Omega$ is $mathbb{R}^n$ or a smooth bounded domain, $k$ is 0 or 1, $l$ is a nonnegative integer, $pin[1,infty)$, and $|.|_{l+sigma,p,Omega}$ is the intrinsic semi-norm of order $l+sigma$ in the Sobolev space $W^{l+sigma,p}(Omega)$. In general, the above limit is equal to $c[v]^p$, where $c$ and $[.]$ are, respectively, a constant and a semi-norm that we explicitly provide. The particular case $p=2$ for $Omega=mathbb{R}^n$ is also examined and the results are then proved by using the Fourier transform." @default.
• W2070851924 created "2016-06-24" @default.
• W2070851924 creator A5006771065 @default.
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• W2070851924 date "2011-11-30" @default.
• W2070851924 modified "2023-10-17" @default.
• W2070851924 title "Limiting behaviour of intrinsic semi-norms in fractional order Sobolev spaces" @default.
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