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arXiv · 2404.09580

The metric for matrix degenerate Kato square root operators

Gianmarco Brocchi·Andreas Rosén
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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 $L^2$-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 $L^2$ spaces, under $W^{1,1}$ homeomorphism.

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Gianmarco Brocchi, Andreas Rosén. 2024-04-15. The metric for matrix degenerate Kato square root operators. https://arxiv.org/abs/2404.09580

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