Limiting behaviour of intrinsic seminorms in fractional order Sobolev spaces

Rémi Arcangéli, and Juan José Torrens. "Limiting behaviour of intrinsic seminorms in fractional order Sobolev spaces." Studia Mathematica 214.2 (2013): 101-120. <http://eudml.org/doc/285895>.

@article{RémiArcangéli2013,
abstract = {We collect and extend results on the limit of $σ^\{1-k\}(1-σ)^\{k\}|v|_\{l+σ,p,Ω\}^\{p\}$ as σ → 0⁺ or σ → 1¯, where Ω is ℝⁿ or a smooth bounded domain, k ∈ 0,1, l ∈ ℕ, p ∈ [1,∞), and $|·|_\{l+σ,p,Ω\}$ is the intrinsic seminorm of order l+σ in the Sobolev space $W^\{l+σ,p\}(Ω)$. In general, the above limit is equal to $c[v]^\{p\}$, where c and [·] are, respectively, a constant and a seminorm that we explicitly provide. The particular case p = 2 for Ω = ℝⁿ is also examined and the results are then proved by using the Fourier transform.},
author = {Rémi Arcangéli, Juan José Torrens},
journal = {Studia Mathematica},
keywords = {Sobolev spaces; fractional-order seminorms; Fourier transform; Beppo Levi spaces},
language = {eng},
number = {2},
pages = {101-120},
title = {Limiting behaviour of intrinsic seminorms in fractional order Sobolev spaces},
url = {http://eudml.org/doc/285895},
volume = {214},
year = {2013},
}

TY - JOUR
AU - Rémi Arcangéli
AU - Juan José Torrens
TI - Limiting behaviour of intrinsic seminorms in fractional order Sobolev spaces
JO - Studia Mathematica
PY - 2013
VL - 214
IS - 2
SP - 101
EP - 120
AB - We collect and extend results on the limit of $σ^{1-k}(1-σ)^{k}|v|_{l+σ,p,Ω}^{p}$ as σ → 0⁺ or σ → 1¯, where Ω is ℝⁿ or a smooth bounded domain, k ∈ 0,1, l ∈ ℕ, p ∈ [1,∞), and $|·|_{l+σ,p,Ω}$ is the intrinsic seminorm of order l+σ in the Sobolev space $W^{l+σ,p}(Ω)$. In general, the above limit is equal to $c[v]^{p}$, where c and [·] are, respectively, a constant and a seminorm that we explicitly provide. The particular case p = 2 for Ω = ℝⁿ is also examined and the results are then proved by using the Fourier transform.
LA - eng
KW - Sobolev spaces; fractional-order seminorms; Fourier transform; Beppo Levi spaces
UR - http://eudml.org/doc/285895
ER -