The Kato square root problem for weighted parabolic operators
Analysis of PDEs
2022-09-23 v1 Classical Analysis and ODEs
Abstract
We give a simplified and direct proof of the Kato square root estimate for parabolic operators with elliptic part in divergence form and coefficients possibly depending on space and time in a merely measurable way. The argument relies on the nowadays classical reduction to a quadratic estimate and a Carleson-type inequality. The precise organization of the estimates is different from earlier works. In particular, we succeed in separating space and time variables almost completely despite the non-autonomous character of the operator. Hence, we can allow for degenerate ellipticity dictated by a spatial -weight, which has not been treated before in this context.
Keywords
Cite
@article{arxiv.2209.11104,
title = {The Kato square root problem for weighted parabolic operators},
author = {Alireza Ataei and Moritz Egert and Kaj Nyström},
journal= {arXiv preprint arXiv:2209.11104},
year = {2022}
}