The metric for matrix degenerate Kato square root operators
Gianmarco Brocchi
University of Iceland, Reykjavík, IcelandAndreas Rosén
Chalmers University of Technology, Göteborg, Sweden; University of Gothenburg, Göteborg, Sweden

Abstract
We prove a Kato square root estimate with anisotropically degenerate matrix coefficients. We do so by doing the harmonic analysis, using an auxiliary Riemannian metric adapted to the operator. We also derive -solvability estimates for boundary value problems, for divergence form elliptic equations with matrix degenerate coefficients. Main tools are chain rules and Piola transformations, for fields in matrix weighted spaces, under homeomorphism.
Cite this article
Gianmarco Brocchi, Andreas Rosén, The metric for matrix degenerate Kato square root operators. Rev. Mat. Iberoam. (2025), published online first
DOI 10.4171/RMI/1572