A constant coefficient Legendre-Hadamard system with no coercive constant coefficient quadratic form over W-1,W-2

摘要

A family of linear homogeneous 2nd order strongly elliptic symmetric systems with real constant coefficients, and bounded nonsmooth convex domains O are constructed in R-6 so that the systems have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces W-1,W-2(Omega). The construction is deduced from the model construction for a 4th order scalar case [Ver14]. The latter is stated and parts of its proof discussed, one particular being the utility of having noncoercive formally positive forms as a starting point. An application of Macaulay's determinantal ideals to the noncoerciveness of formally positive forms for systems is then given.