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Zeitschrift für Analysis und ihre Anwendungen


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Volume 17, Issue 3, 1998, pp. 565–575
DOI: 10.4171/ZAA/839

Published online: 1998-09-30

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

O. Zaytsev[1]

(1) University of Latvia, Riga, Latvia

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.

Keywords: Strong closure, feasible states, elliptic operators, systems of elliptic equations

Zaytsev O.: On Strong Closure of Sets of Feasible States Associated with Families of Elliptic Operators. Z. Anal. Anwend. 17 (1998), 565-575. doi: 10.4171/ZAA/839