arXiv 0810.30712008-10math.CAmath.APmath.FA

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

Pascal Auscher, Andreas Axelsson, Alan McIntosh

备注：: Text of the lectures given at the El Escorial 2008 conference. Revised after the suggestions of the referee. Some historical material added. A short proof of the main result added under a further assumption. To appear in the Proceedings

英文摘要：

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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