Publicacions Matemàtiques

The Kato square root problem follows from an extrapolation property of the Laplacian

Moritz Egert, Robert Haller-Dintelmann, and Patrick Tolksdorf

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Abstract

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.

Article information

Source
Publ. Mat. Volume 60, Number 2 (2016), 451-483.

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

Permanent link to this document
https://projecteuclid.org/euclid.pm/1468242040

Digital Object Identifier
doi:10.5565/PUBLMAT_60216_05

Mathematical Reviews number (MathSciNet)
MR3521496

Zentralblatt MATH identifier
1349.35112

Subjects
Primary: 35J57: Boundary value problems for second-order elliptic systems 47A60: Functional calculus 42B37: Harmonic analysis and PDE [See also 35-XX]

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

Citation

Egert, Moritz; Haller-Dintelmann, Robert; Tolksdorf, Patrick. The Kato square root problem follows from an extrapolation property of the Laplacian. Publ. Mat. 60 (2016), no. 2, 451--483. doi:10.5565/PUBLMAT_60216_05. https://projecteuclid.org/euclid.pm/1468242040.


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