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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.12741 |
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| _version_ | 1866913057030012928 |
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| author | Pathak, Aritro |
| author_facet | Pathak, Aritro |
| contents | We introduce a technique to obtain pointwise upper and lower bounds for the Green's function of elliptic operators whose principal part is the Laplacian and that include a drift term diverging near the boundary like a power of the inverse distance with exponent less than 1, in the unit ball B(0,1) \subset \mathbb{R}^n, n \ge 3. The constants in the upper estimates are uniform in B(0,r) for each r < 1, with explicit dependence on r. The drift here belongs to C^{1,α}_{\mathrm{loc}} and may, more generally, be majorized by a function radially integrable up to the boundary. These appear to be the first such estimates for non-coercive drifts and remain new even for smooth drifts, suggesting extensions to singular potentials and other settings where energy methods fail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12741 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pointwise bounds on Dirichlet Green's functions for a singular drift term Pathak, Aritro Analysis of PDEs We introduce a technique to obtain pointwise upper and lower bounds for the Green's function of elliptic operators whose principal part is the Laplacian and that include a drift term diverging near the boundary like a power of the inverse distance with exponent less than 1, in the unit ball B(0,1) \subset \mathbb{R}^n, n \ge 3. The constants in the upper estimates are uniform in B(0,r) for each r < 1, with explicit dependence on r. The drift here belongs to C^{1,α}_{\mathrm{loc}} and may, more generally, be majorized by a function radially integrable up to the boundary. These appear to be the first such estimates for non-coercive drifts and remain new even for smooth drifts, suggesting extensions to singular potentials and other settings where energy methods fail. |
| title | Pointwise bounds on Dirichlet Green's functions for a singular drift term |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.12741 |