On strong closure of the graphs associated with families of elliptic operators

Abstract

The closures of the graphs associated with families of elliptic operators, corresponding to systems of elliptic equations, in the strong topology of the Cartesian product of Sobolev spaces are considered. For a sufficiently general class of families of elliptic operators which are encountered in problems of optimal layout of r materials (r ≥ 2) it is shown that if the number m of unknown functions is greater than or equal to the number n of independent variables and n ≥ 2, it is, in general, impossible to parametrize the strong closures of graphs associated with families from this class by means of families of continuous linear operators.

Keywords:

• strong closure
• graph
• elliptic operators