Sharp order of vanishing for parabolic equations, nodal set estimates and Landis type results
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914804716797952 |
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| author | Arya, Vedansh Banerjee, Agnid Garofalo, Nicola |
| author_facet | Arya, Vedansh Banerjee, Agnid Garofalo, Nicola |
| contents | We establish a new sharp estimate of the order of vanishing of solutions to parabolic equations with variable coefficients. For real-analytic leading coefficients, we prove a localised estimate of the nodal set, at a given time-level, that generalises the celebrated one of Donnelly and Fefferman. We also establish Landis type results for global solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13253 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp order of vanishing for parabolic equations, nodal set estimates and Landis type results Arya, Vedansh Banerjee, Agnid Garofalo, Nicola Analysis of PDEs We establish a new sharp estimate of the order of vanishing of solutions to parabolic equations with variable coefficients. For real-analytic leading coefficients, we prove a localised estimate of the nodal set, at a given time-level, that generalises the celebrated one of Donnelly and Fefferman. We also establish Landis type results for global solutions. |
| title | Sharp order of vanishing for parabolic equations, nodal set estimates and Landis type results |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.13253 |