On a quadratic estimate related to the Kato conjecture and boundary value problems

  title={On a quadratic estimate related to the Kato conjecture and boundary value problems},
  author={P. Auscher and A. Axelsson and A. McIntosh},
  journal={arXiv: Classical Analysis and ODEs},
  • P. Auscher, A. Axelsson, A. McIntosh
  • Published 2010
  • Mathematics
  • arXiv: Classical Analysis and ODEs
  • We provide a direct proof of a quadratic estimate that plays a central role in the determination of domains of square roots of elliptic operators and, as shown more recently, in some boundary value problems with $L^2$ boundary data. We develop the application to the Kato conjecture and to a Neumann problem. This quadratic estimate enjoys some equivalent forms in various settings. This gives new results in the functional calculus of Dirac type operators on forms. 
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