A stability result for parabolic measures of operators with singular drifts
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917867184717824 |
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| author | Bortz, Simon Egert, Moritz Saari, Olli |
| author_facet | Bortz, Simon Egert, Moritz Saari, Olli |
| contents | We study the operator \[ \partial_t - \text{div} A \nabla + B \cdot \nabla \] in parabolic upper-half-space, where $A$ is an elliptic matrix satisfying an oscillation condition and $B$ is a singular drift with a Carleson control. Our main result establishes quantitative $A_{\infty}$-estimates for the parabolic measure in terms of oscillation of $A$ and smallness of $B$. The proof relies on new estimates for parabolic Green functions that quantify their deviations from linear functions of the normal variable and on a novel, quantitative Carleson measure criterion for anisotropic $A_{\infty}$-weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A stability result for parabolic measures of operators with singular drifts Bortz, Simon Egert, Moritz Saari, Olli Analysis of PDEs Classical Analysis and ODEs We study the operator \[ \partial_t - \text{div} A \nabla + B \cdot \nabla \] in parabolic upper-half-space, where $A$ is an elliptic matrix satisfying an oscillation condition and $B$ is a singular drift with a Carleson control. Our main result establishes quantitative $A_{\infty}$-estimates for the parabolic measure in terms of oscillation of $A$ and smallness of $B$. The proof relies on new estimates for parabolic Green functions that quantify their deviations from linear functions of the normal variable and on a novel, quantitative Carleson measure criterion for anisotropic $A_{\infty}$-weights. |
| title | A stability result for parabolic measures of operators with singular drifts |
| topic | Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2412.09301 |