Strongly elliptic linear operators without coercive quadratic forms. I. Constant coefficient operators and forms

Abstract

A family of linear homogeneous 4th order elliptic differential operators $L$ with real constant coefficients, and bounded nonsmooth convex domains $\Omega$ are constructed in $\mathbb{R}^6$ so that the $L$ have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces $W^{2,2}(\Omega)$.