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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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