Geodesic
Strongly elliptic linear operators without coercive quadratic forms. I. Constant coefficient operators and forms
Journal of the European Mathematical Society, Tome 16 (2014) no. 10, pp. 2165-2210

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A family of linear homogeneous 4th order elliptic differential operators L with real constant coefficients, and bounded nonsmooth convex domains Ω are constructed in R6 so that the L have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces W2,2(Ω).
DOI : 10.4171/jems/485
Classification : 35-XX, 00-XX, 15-XX
Keywords: Neumann problem, Rellich identity, Legendre–Hadamard, Korn inequality, Lax–Milgram, sum of squares, null form, indefinite form 
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     author = {Gregory C. Verchota},
     title = {Strongly elliptic linear operators without coercive quadratic forms. {I.} {Constant} coefficient operators and forms},
     journal = {Journal of the European Mathematical Society},
     pages = {2165--2210},
     publisher = {mathdoc},
     volume = {16},
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     year = {2014},
     doi = {10.4171/jems/485},
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Gregory C. Verchota. Strongly elliptic linear operators without coercive quadratic forms. I. Constant coefficient operators and forms. Journal of the European Mathematical Society, Tome 16 (2014) no. 10, pp. 2165-2210. doi: 10.4171/jems/485

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