The metric for matrix degenerate Kato square root operators

  • Gianmarco Brocchi

    University of Iceland, Reykjavík, Iceland
  • Andreas Rosén

    Chalmers University of Technology, Göteborg, Sweden; University of Gothenburg, Göteborg, Sweden
The metric for matrix degenerate Kato square root operators cover
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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