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

Research output: Contribution to journalArticle

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Abstract

A family of linear homogeneous fourth 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).

Original languageEnglish (US)
Pages (from-to)2165-2210
Number of pages46
JournalJournal of the European Mathematical Society
Volume16
Issue number10
DOIs
StatePublished - Jan 1 2014

Keywords

  • Indefinite form
  • Korn inequality
  • Lax-Milgram
  • Legendre-Hadamard
  • Neumann problem
  • Null form
  • Rellich identity
  • Sum of squares

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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