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.

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.