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

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

2008-10-17

arxiv.org/abs/0810.3071v2

Mathematics

Classical Analysis and ODEs

Text of the lectures given at the El Escorial 2008 conference. Revised after the suggestions of the referee. Some historical m

Scientific paper

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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