# On Strong Closure of Sets of Feasible States Associated with Families of Elliptic Operators

### O. Zaytsev

University of Latvia, Riga, Latvia

## Abstract

The closure of sets of feasible states for systems of elliptic equations in the strong topology of the Cartesian product $[H^1_0 (\Omega)]^m$ of Sobolev spaces is considered. For $m = 2$ and $\Omega \subset \mathbb R^2$, it is shown that there is a family of linear elliptic operators of the type div $(\chi \mathcal A^1 + (1 - \chi)\mathcal A^2)\triangledown$, where $\chi$ belongs to the set of all characteristic functions of measurable subsets of $\Omega$, such that there does not exist a larger family of operators of the type div $\mathcal A \triangledown$ for which the sets of feasible states coincide with the closure of the original ones.

## Cite this article

O. Zaytsev, On Strong Closure of Sets of Feasible States Associated with Families of Elliptic Operators. Z. Anal. Anwend. 17 (1998), no. 3, pp. 565–575

DOI 10.4171/ZAA/839