## Publicacions Matemàtiques

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

#### 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
Revised: 2 March 2015
First available in Project Euclid: 11 July 2016

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

#### 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