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

Research paper by Pascal Auscher, Andreas Axelsson, Alan McIntosh

Indexed on: 17 May '09Published on: 17 May '09Published in: Mathematics - Classical Analysis and ODEs



Abstract

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.