On the range of elliptic operators discontinuous at one point

Giannotti, Cristina

Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 1, pp. 123-129

Résumé

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 $p\in(1, d/2 ]$.