Journal d’Analyse Mathématique

, Volume 90, Issue 1, pp 1–12 | Cite as

Square roots of elliptic second order divergence operators on strongly lipschitz domains:L 2 theory

  • P. Auscher
  • PH. Tchamitchian


We prove the Kato conjecture for square roots of elliptic second order non-self-adjoint operators in divergence formL = -div(A∇) on strongly Lipschitz domains in ℝn, n≥2, subject to Dirichlet or to Neumann boundary conditions. The method relies on a transference procedure from the recent positive result on ℝn in [2].


Elliptic Operator Neumann Boundary Condition Lipschitz Domain Comparison Principle Carleson Measure 
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Copyright information

© Hebrew University of Jerusalem 2003

Authors and Affiliations

  • P. Auscher
    • 1
  • PH. Tchamitchian
    • 2
    • 3
  1. 1.Laboratoire de Mathématiques CNRS UMR 8628Université de Paris-SudOrsay CedexFrance
  2. 2.Faculté des Sciences et Techniques de Saint-JérÔmeUniversité d’Aix-Marseille IIIMarseille Cedex 20France
  3. 3.LATP, CNRSFrance

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