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2016 The Kato square root problem follows from an extrapolation property of the Laplacian
Moritz Egert, Robert Haller-Dintelmann, Patrick Tolksdorf
Publ. Mat. 60(2): 451-483 (2016). DOI: 10.5565/PUBLMAT_60216_05


On a domain $\Omega \subseteq \mathbb{R}^d$ we consider second-order elliptic systems in divergence-form with bounded complex coefficients, realized via a sesquilinear form with domain $\mathrm{H}_0^1(\Omega) \subseteq \mathcal{V} \subseteq \mathrm{H}^1(\Omega)$. Under very mild assumptions on~$\Omega$ and $\mathcal{V}$ we show that the solution to the Kato Square Root Problem for such systems can be deduced from a regularity result for the fractional powers of the negative Laplacian in the same geometric setting. This extends earlier results of McIntosh [25] and Axelsson-Keith-McIntosh [6] to non-smooth coefficients and domains.


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Moritz Egert. Robert Haller-Dintelmann. Patrick Tolksdorf. "The Kato square root problem follows from an extrapolation property of the Laplacian." Publ. Mat. 60 (2) 451 - 483, 2016.


Received: 4 September 2014; Revised: 2 March 2015; Published: 2016
First available in Project Euclid: 11 July 2016

zbMATH: 1349.35112
MathSciNet: MR3521496
Digital Object Identifier: 10.5565/PUBLMAT_60216_05

Primary: 35J57 , 42B37 , 47A60

Keywords: Carleson measures , functional calculus , Kato's Square Root Problem , quadratic estimates , sectorial and bisectorial operators

Rights: Copyright © 2016 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.60 • No. 2 • 2016
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