Square roots of elliptic second order divergence operators on strongly Lipschitz domains:
$L^p$ theory |
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Authors: | P Auscher Ph Tchamitchian |
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Institution: | Faculté de mathématiques et d'Informatique, 33, rue Saint Leu, F-80039 Amiens Cedex 1, France, and LAMFA, CNRS, FRE 2270 (e-mail: auscher@u-picardie.fr), FR Faculté des Sciences et Techniques de Saint-Jér?me, Avenue Escadrille Normandie-Niemen, F-13397 Marseille Cedex 20, France, and LATP, CNRS, UMR 6632 (e-mail: tchamphi@math.u-3mrs.fr), FR
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Abstract: | We study estimates for square roots of second order elliptic non necessarily selfadjoint operators in divergence form on Lipschitz domains subject to Dirichlet or to Neumann boundary conditions, pursuing our work 4] where we considered operators
on . We obtain among other things for all if L is real symmetric and the domain bounded, which is new for . We also obtain similar results for perturbations of constant coefficients operators. Our methods rely on a singular integral
representation, Calderón-Zygmund theory and quadratic estimates. A feature of this study is the use of a commutator between
the resolvent of the Laplacian (Dirichlet and Neumann) and partial derivatives which carries the geometry of the boundary.
Received: 12 January 2000 / Published online: 4 May 2001 |
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Keywords: | |
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