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

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Abstract

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].

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Authors and Affiliations

  1. Laboratoire de Mathématiques CNRS UMR 8628, Université de Paris-Sud, F-91405, Orsay Cedex, France

    P. Auscher

  2. Faculté des Sciences et Techniques de Saint-JérÔme, Université d’Aix-Marseille III, Avenue Escadrille Normandie-Niemen, F-13397, Marseille Cedex 20, France

    PH. Tchamitchian

  3. LATP, CNRS, UMR 6632, France

    PH. Tchamitchian

Authors
  1. P. Auscher
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  2. PH. Tchamitchian
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Auscher, P., Tchamitchian, P. Square roots of elliptic second order divergence operators on strongly lipschitz domains:L 2 theory. J. Anal. Math. 90, 1–12 (2003). https://doi.org/10.1007/BF02786549

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  • DOI: https://doi.org/10.1007/BF02786549

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