Geodesic
On the range of elliptic operators discontinuous at one point
Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 1, pp. 123-129.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Let $L$ be a second order, uniformly elliptic, non variational operator with coefficients which are bounded and measurable in $\mathbb{R}^{d}$ ($d\geq3$) and continuous in $\mathbb{R}^{d} \setminus \{0\}$. Then, if $\Omega\subset \mathbb{R}^{d}$ is a bounded domain, we prove that $L(W^{2, p }(\Omega))$ is dense in $L^{p}(\Omega)$ 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 $\mathbb{R}^{d}$ ($d \geq 3$) e continui in $\mathbb{R}^{d} \setminus \{0\}$ e si prova il seguente risultato: se $\Omega\subset \mathbb{R}^{d}$ è un dominio limitato, allora $L(W^{2, p}(\Omega))$ è denso in $L^{p}(\Omega)$ per ogni $p\in (1, d/2]$. 
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Giannotti, Cristina. On the range of elliptic operators discontinuous at one point. Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 1, pp. 123-129. http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_1_a4/

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