A family of linear homogeneous 4th order elliptic differential operators with real constant coefficients, and bounded nonsmooth convex domains are constructed in so that the have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces .
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Gregory C. Verchota, Strongly elliptic linear operators without coercive quadratic forms. I. Constant coefficient operators and forms. J. Eur. Math. Soc. 16 (2014), no. 10, pp. 2165–2210DOI 10.4171/JEMS/485