A limit involving functions in $W_0^{1,p}\left(\Omega \right)$

Ricceri, Biagio. "A limit involving functions in $W^{1,p}_0(Ω)$." Colloquium Mathematicae 82.2 (1999): 219-222. <http://eudml.org/doc/210758>.

@article{Ricceri1999,
abstract = {We point out the following fact: if Ω ⊂ $ℝ^n$ is a bounded open set, δ>0, and p>1, then $lim_\{ → 0^+\} inf_\{ ∈ V_\} ∫_Ω |∇(x)|^p dx=∞$, where $V_=\{ ∈ W^\{1,p\}_0(Ω): meas (\{x ∈ Ω:|(x)|>δ\})>\}.$},
author = {Ricceri, Biagio},
journal = {Colloquium Mathematicae},
keywords = {Sobolev spaces on bounded domains; subatomic decompositions; Schwartz space; Taylor expansions},
language = {eng},
number = {2},
pages = {219-222},
title = {A limit involving functions in $W^\{1,p\}_0(Ω)$},
url = {http://eudml.org/doc/210758},
volume = {82},
year = {1999},
}

TY - JOUR
AU - Ricceri, Biagio
TI - A limit involving functions in $W^{1,p}_0(Ω)$
JO - Colloquium Mathematicae
PY - 1999
VL - 82
IS - 2
SP - 219
EP - 222
AB - We point out the following fact: if Ω ⊂ $ℝ^n$ is a bounded open set, δ>0, and p>1, then $lim_{ → 0^+} inf_{ ∈ V_} ∫_Ω |∇(x)|^p dx=∞$, where $V_={ ∈ W^{1,p}_0(Ω): meas ({x ∈ Ω:|(x)|>δ})>}.$
LA - eng
KW - Sobolev spaces on bounded domains; subatomic decompositions; Schwartz space; Taylor expansions
UR - http://eudml.org/doc/210758
ER -