• DOI:10.1090/CONM/505
Corpus ID: 5766259

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

@article{Auscher2010OnAQ,
  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},
  year={2010},
  volume={505}
}

P. Auscher, A. Axelsson, A. McIntosh

Published 2010

Mathematics

arXiv: Classical Analysis and ODEs

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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.