English

The Kato problem for weighted elliptic and parabolic operators of higher order

Analysis of PDEs 2025-11-10 v4

Abstract

We solve the Kato square root problem for parabolic operators of arbitrary order 2m2m whose coefficients are allowed to depend on both space and time in a merely measurable way and possess boundedness and ellipticity controlled by a Muckenhoupt A2A_{2}-weight. Notably, the proof applies to the weighted Kato problem within an elliptic framework.

Keywords

Cite

@article{arxiv.2503.01636,
  title  = {The Kato problem for weighted elliptic and parabolic operators of higher order},
  author = {Guoming Zhang},
  journal= {arXiv preprint arXiv:2503.01636},
  year   = {2025}
}