JournalsjemsVol. 16, No. 10pp. 2165–2210

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

  • Gregory C. Verchota

    Syracuse University, USA
Strongly elliptic linear operators without coercive quadratic forms. I. Constant coefficient operators and forms cover
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Abstract

A family of linear homogeneous 4th order elliptic differential operators LL with real constant coefficients, and bounded nonsmooth convex domains Ω\Omega are constructed in R6\mathbb{R}^6 so that the LL have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces W2,2(Ω)W^{2,2}(\Omega).

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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. 2165–2210

DOI 10.4171/JEMS/485