JournalszaaVol. 17, No. 3pp. 565–575

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

  • O. Zaytsev

    University of Latvia, Riga, Latvia
On Strong Closure of Sets of Feasible States Associated with Families of Elliptic Operators cover
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Abstract

The closure of sets of feasible states for systems of elliptic equations in the strong topology of the Cartesian product [H01(Ω)]m[H^1_0 (\Omega)]^m of Sobolev spaces is considered. For m=2m = 2 and ΩR2\Omega \subset \mathbb R^2, it is shown that there is a family of linear elliptic operators of the type div (χA1+(1χ)A2)(\chi \mathcal A^1 + (1 - \chi)\mathcal A^2)\triangledown, where χ\chi belongs to the set of all characteristic functions of measurable subsets of Ω\Omega, such that there does not exist a larger family of operators of the type div A\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