On the range of elliptic operators discontinuous at one point

Giannotti, Cristina

Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002), p. 123-129 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

Let $L$ be a second order, uniformly elliptic, non variational operator with coefficients which are bounded and measurable in $R^{d}$ ( $d \geq 3$ ) and continuous in $R^{d} ∖ \{0\}$ . Then, if $Ω \subset R^{d}$ is a bounded domain, we prove that $L (W^{2, p} (Ω))$ is dense in $L^{p} (Ω)$ for any $p \in (1, d / 2]$ .

Si considerano operatori uniformemente ellittici del secondo ordine in forma non variazionale, $L$ , a coefficienti misurabili e limitati in $R^{d}$ ( $d \geq 3$ ) e continui in $R^{d} ∖ \{0\}$ e si prova il seguente risultato: se $Ω \subset R^{d}$ è un dominio limitato, allora $L (W^{2, p} (Ω))$ è denso in $L^{p} (Ω)$ per ogni $p \in (1, d / 2]$ .

Publié le : 2002-02-01

MR 1881447 | Zbl 1178.47032

@article{BUMI_2002_8_5B_1_123_0,
     author = {Cristina Giannotti},
     title = {On the range of elliptic operators discontinuous at one point},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {5-A},
     year = {2002},
     pages = {123-129},
     zbl = {1178.47032},
     mrnumber = {1881447},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2002_8_5B_1_123_0}
}

Giannotti, Cristina. On the range of elliptic operators discontinuous at one point. Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002) pp. 123-129. http://gdmltest.u-ga.fr/item/BUMI_2002_8_5B_1_123_0/

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