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

arXiv eprints
 Pub Date:
 October 2008
 arXiv:
 arXiv:0810.3071
 Bibcode:
 2008arXiv0810.3071A
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematics  Analysis of PDEs;
 Mathematics  Functional Analysis;
 35J25;
 35J55;
 47N20;
 47F05;
 42B25
 EPrint:
 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