Heat kernel estimates for Schrödinger operators with supercritical killing potentials
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929690507214848 |
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| author | Cho, Soobin Kim, Panki Song, Renming |
| author_facet | Cho, Soobin Kim, Panki Song, Renming |
| contents | In this paper, we study the Schrödinger operator $Δ-V$, where $V$ is a supercritical non-negative potential belonging to a large class of functions containing functions of the form $b|x|^{-(2+2β)}$, $b, β>0$. We obtain two-sided estimates on the heat kernel $p(t, x, y)$ of $Δ-V$, along with estimates for the corresponding Green function. Unlike the case of the fractional Schrödinger operator $-(-Δ)^{α/2}-V$, $α\in (0, 2)$, with supercritical killing potential dealt with in [11], in the present case, the heat kernel $p(t, x, y)$ decays to 0 exponentially as $x$ or $y$ tends to the origin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heat kernel estimates for Schrödinger operators with supercritical killing potentials Cho, Soobin Kim, Panki Song, Renming Probability Analysis of PDEs 47D08, 60J35, 60J65, 35K08 In this paper, we study the Schrödinger operator $Δ-V$, where $V$ is a supercritical non-negative potential belonging to a large class of functions containing functions of the form $b|x|^{-(2+2β)}$, $b, β>0$. We obtain two-sided estimates on the heat kernel $p(t, x, y)$ of $Δ-V$, along with estimates for the corresponding Green function. Unlike the case of the fractional Schrödinger operator $-(-Δ)^{α/2}-V$, $α\in (0, 2)$, with supercritical killing potential dealt with in [11], in the present case, the heat kernel $p(t, x, y)$ decays to 0 exponentially as $x$ or $y$ tends to the origin. |
| title | Heat kernel estimates for Schrödinger operators with supercritical killing potentials |
| topic | Probability Analysis of PDEs 47D08, 60J35, 60J65, 35K08 |
| url | https://arxiv.org/abs/2501.17440 |