Approximation by solutions of elliptic equations
Let \(\Omega\) be a bounded smooth domain in \({\mathbb{R}}^ n\), \(\Gamma\) a closed smooth (n-1)-dimensional surface with boundary in the interior of \(\Omega\), V an open subset of \(\partial \Omega\), L an 2m-order properly elliptic operator with smooth coefficients, and \((B_ 1,...,B_ m)\) a normal system of boundary operators on \(\partial \Omega\). The author proves that the set of all \(C^{\infty}({\bar \Omega})\)-solutions of \(Lu=0\), \(B_ ju|_{\partial \Omega}=0\) on \(\partial \Omega \setminus V\), is dense in \(W_ p^{2m-1/p}(\Gamma)\) for \(p>1\).
scientific article; zbMATH DE number 3953403