Abstract
A family of linear homogeneous 2nd order strongly elliptic symmetric systems with real constant coefficients, and bounded nonsmooth convex domains Ω are constructed in ℝ6 so that the systems have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces W1,2(Ω). 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.
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 - 2015 |
Keywords
- Determinantal ideal
- Indefinite form
- Korn's inequality
- Neumann problem
- Null form
- Rellich identity
- Strongly elliptic
- Sum of squares
ASJC Scopus subject areas
- General Mathematics