Existence of weak solutions to linear indefinite systems of differential equations (Q1089525)

The motivation for this paper came from the linearised theory of elasticity. The author discusses the question of the existence of solutions to an abstract problem ü-\(Cu=f\) which corresponds to the case of indefinite elasticities. The approach is based on a decomposition of \(L^ 2(\Omega)\) into the direct sum of two invariant subspaces \(H_+\) and \(H_-\), on each of which the equation becomes definite. On the base of this decomposition the author defines two operators \(A_+\) and \(A_- \), and using techniques familiar in the theory of elliptic and hyperbolic operators, he shows that these operators are closed. This fact leads to the main result: In a certain weak sense a solution exists for a dense set of data.