Square roots of elliptic second order divergence operators on strongly lipschitz domains:L 2 theory
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 .
KeywordsElliptic Operator Neumann Boundary Condition Lipschitz Domain Comparison Principle Carleson Measure
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