|
|||||
|
|
The Kato square root problem for higher order elliptic operators and systems on $ \Bbb R^n $ |
|
| Authors: | Pascal Auscher Steve Hofmann Alan McIntosh Philippe Tchamitchian |
| Institution: | (1) LAMIA, CNRS, FRE 2270, Université de Picardie-Jules Verne, 33, rue Saint Leu, 80039 Amiens Cedex 1, e-mail: auscher@mathinfo.u-picardie.fr, FR;(2) Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, e-mail: hofmann@math.missouri.edu, US;(3) Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, e-mail: alan@maths.anu.edu.au, AT;(4) Faculté des Sciences et, Techniques de St.-Jérome, Université d'Aix-Marseille III, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, and LATP, CNRS, UMR 6632, e-mail: tchamphi@math.u-3mrs.fr, FR |
| Abstract: | We prove the Kato conjecture for elliptic operators and N×N-systems in divergence form of arbitrary order 2m on . More precisely, we assume the coefficients to be bounded measurable and the ellipticity is taken in the sense of a G?rding inequality. We identify the domain of their square roots as the natural Sobolev space . We also make some remarks on the relation between various ellipticity conditions and G?rding inequality. Received May 4, 2001; accepted September 6, 2001. |
| Keywords: | : Elliptic systems G?rding inequality Kato problem square roots |
| 本文献已被 SpringerLink 等数据库收录！ | |