English

On the Kato problem for elliptic operators in non-divergence form

Analysis of PDEs 2023-10-06 v3 Classical Analysis and ODEs

Abstract

We consider the Kato square root problem for non-divergence second order elliptic operators L=aijDiDjL =- a_{ij} D_iD_j, and, especially, the normalized adjoints of such operators. In particular, our results are applicable to the case of real coefficients having sufficiently small BMO norm. We assume that the coefficients of the operator are smooth, but our estimates do not depend on the assumption of smoothness.

Keywords

Cite

@article{arxiv.2304.14694,
  title  = {On the Kato problem for elliptic operators in non-divergence form},
  author = {Luis Escauriaza and Pablo Hidalgo-Palencia and Steve Hofmann},
  journal= {arXiv preprint arXiv:2304.14694},
  year   = {2023}
}

Comments

30 pages. In this version, we have added more details in Remark 1.12

R2 v1 2026-06-28T10:20:32.640Z