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

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.

The implicit constants in Propositions 4.4 and 4.5 depend on $\alpha$. An alternative proof is needed in order to use the approximation arguments of Section 5. arXiv admin note: text overlap with arXiv:1812.10196

References in corpus (1)

• The Kato Square Root Problem on Submanifolds