Work

The metric for matrix degenerate Kato square root operators

Year: 2025

Type: article

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.

Source: Revista Matemática Iberoamericana

DOI: 10.4171/rmi/1572

Authors: Gianmarco Brocchi, Andreas Rosén

Institutions: University of Iceland, Chalmers University of Technology, University of Gothenburg

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Knut och Alice Wallenbergs Stiftelse, Vetenskapsrådet

Award: Sparse domination for boundary value problems