Approximation durch Lösungen elliptischer Randwertprobleme auf offenen Mengen. II. (Approximation by solutions of elliptic boundary value problems on open sets. II) (Q1190758)

In Part I [see ibid. 9, No. 4, 289-301 (1990; Zbl 0725.35040)] the author studied an approximation problem in Sobolev spaces. In this part he studies the \(C^ k (\overline\Omega_ 1)\) approximation of solutions of the homogeneous differential equation in \(\Omega_ 1\). Let \(\Omega \subset \mathbb{R}^ n\) be a bounded, smooth domain, \(\Omega_ 1 \subset \overline\Omega_ 1\subset \Omega\) an arbitrary domain and \(L\) an elliptic differential operator on \(\Omega\). It is proved that every function \(v \in C^ k (\overline\Omega_ 1)\) \((0 \leq k<\infty)\) with \(Lv=0\) in \(\Omega_ 1\) can be approximated in the \(C^ k (\overline\Omega_ 1)\)-norm by solutions of elliptic boundary value problems with respet to \(\Omega\) if \(\Omega_ 1\) has the restricted cone property.