Agmon Coerciveness and the Analysis of Operators with Formally Positive Integro-Differential Forms

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2 Scopus citations

Abstract

For Sobolev spaces in Lipschitz domains with no imposed boundary conditions, the Aronszajn-Smith theorem algebraically characterizes coercive formally positive integro-differential quadratic forms. Recently, linear elliptic differential operators with formally positive forms have been constructed with the property that no formally positive forms for these operators can be coercive in any bounded domain. In the present article 4th order operators of this kind are shown by perturbation to have coercive forms that are (necessarily) algebraically indefinite. The perturbation here from noncoercive formally positive forms to coercive algebraically indefinite forms requires Agmon's characterization of coerciveness in smoother domains than Lipschitz.

Original languageEnglish (US)
Pages (from-to)285-297
Number of pages13
JournalCommunications in Partial Differential Equations
Volume37
Issue number2
DOIs
StatePublished - Feb 1 2012

Keywords

  • Aronszajn-Smith
  • Indefinite form
  • Lax-Milgram
  • Neuman problems
  • Sum of squares

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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