Limiting behaviour of intrinsic seminorms in fractional order Sobolev spaces

Rémi Arcangéli ; Juan José Torrens

Studia Mathematica, Tome 215 (2013), p. 101-120 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2013-01-01

Zbl 1284.46026

EUDML-ID : urn:eudml:doc:285895