# The Kato square root problem on an arbitrary domain of $\mathbb{R}^d$

## TL;DR

This paper resolves the Kato square root problem for a broad class of elliptic operators with complex coefficients on arbitrary Euclidean domains, including boundary conditions and potential perturbations.

## Contribution

It extends the solution of the Kato problem to general domains with measurable, complex coefficients and includes boundary conditions and potential perturbations.

## Key findings

- Solved the Kato square root problem on arbitrary domains
- Extended results to operators with complex coefficients and potentials
- Applicable to Dirichlet boundary conditions

## Abstract

We solve the Kato square root problem for general elliptic operators and systems with measurable and complex coefficients on any domain of the Euclidean space. The operators are subject to Dirichlet boundary conditions. We also allow perturbations by general complex potentials.

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Source: https://tomesphere.com/paper/1902.01101