A limit involving functions in $W^{1,p}_0(Ω)$

Ricceri, Biagio

A limit involving functions in

W_{0}^{1, p} (Ω)

Ricceri, Biagio

Colloquium Mathematicae, Tome 79 (1999), p. 219-222 / Harvested from The Polish Digital Mathematics Library

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Résumé

We point out the following fact: if Ω ⊂ $ℝ^{n}$ is a bounded open set, δ>0, and p>1, then $l i m_{\to 0^{+}} i n f_{\in V} \int_{Ω} {| \nabla (x) |}^{p} d x = \infty$ , where $V_{=} \in W_{0}^{1, p} (Ω) : m e a s (x \in Ω : | (x) | > δ) > .$

Publié le : 1999-01-01

Zbl 0954.46023

EUDML-ID : urn:eudml:doc:210758

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     author = {Biagio Ricceri},
     title = {A limit involving functions in $W^{1,p}\_0($\Omega$)$
            },
     journal = {Colloquium Mathematicae},
     volume = {79},
     year = {1999},
     pages = {219-222},
     zbl = {0954.46023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv82i2p219bwm}
}

Ricceri, Biagio. A limit involving functions in $W^{1,p}_0(Ω)$
            . Colloquium Mathematicae, Tome 79 (1999) pp. 219-222. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv82i2p219bwm/

Bibliographie

[000] [1] H. Brézis, Analyse fonctionnelle, Masson, 1983.

[001] [2] V. G. Maz'ja, Sobolev Spaces, Springer, 1985.