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Mathematics > Analysis of PDEs
Title: The metric for matrix degenerate Kato square root operators
(Submitted on 15 Apr 2024)
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.
Submission history
From: Gianmarco Brocchi [view email][v1] Mon, 15 Apr 2024 08:42:39 GMT (929kb,D)
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