The metric for matrix degenerate Kato square root operators
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909622594437120 |
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| author | Brocchi, Gianmarco Rosén, Andreas |
| author_facet | Brocchi, Gianmarco Rosén, Andreas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09580 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The metric for matrix degenerate Kato square root operators Brocchi, Gianmarco Rosén, Andreas Analysis of PDEs Classical Analysis and ODEs 42B37, 35J70, 58J32, 35J56, 35J57, 47B12 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. |
| title | The metric for matrix degenerate Kato square root operators |
| topic | Analysis of PDEs Classical Analysis and ODEs 42B37, 35J70, 58J32, 35J56, 35J57, 47B12 |
| url | https://arxiv.org/abs/2404.09580 |