### Abstract

A family of linear homogeneous 2^{nd} order strongly elliptic symmetric systems with real constant coefficients, and bounded nonsmooth convex domains Ω are constructed in ℝ^{6} so that the systems have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces W^{1,2}(Ω). The construction is deduced from the model construction for a 4^{th} 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.

Original language | English (US) |
---|---|

Pages (from-to) | 945-965 |

Number of pages | 21 |

Journal | Mathematical Research Letters |

Volume | 22 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2015 |

### Keywords

- Determinantal ideal
- Indefinite form
- Korn's inequality
- Neumann problem
- Null form
- Rellich identity
- Strongly elliptic
- Sum of squares

### ASJC Scopus subject areas

- Mathematics(all)