Two-sided Gaussian estimates for fundamental solutions of second-order parabolic equations in non-divergence form
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916742860636160 |
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| author | Kim, Seick Lee, Sungjin Sakellaris, Georgios |
| author_facet | Kim, Seick Lee, Sungjin Sakellaris, Georgios |
| contents | We establish two-sided Gaussian bounds for the fundamental solution of second-order parabolic operators in non-divergence form under minimal regularity assumptions. Specifically, we show that the upper and lower bounds follow from the local boundedness property and the weak Harnack inequality for the adjoint operator $P^*$, respectively. This provides a simpler and more direct proof of the Gaussian estimates when the coefficients have Dini mean oscillation in $x$, avoiding the use of normalized adjoint solutions required in previous works. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-sided Gaussian estimates for fundamental solutions of second-order parabolic equations in non-divergence form Kim, Seick Lee, Sungjin Sakellaris, Georgios Analysis of PDEs We establish two-sided Gaussian bounds for the fundamental solution of second-order parabolic operators in non-divergence form under minimal regularity assumptions. Specifically, we show that the upper and lower bounds follow from the local boundedness property and the weak Harnack inequality for the adjoint operator $P^*$, respectively. This provides a simpler and more direct proof of the Gaussian estimates when the coefficients have Dini mean oscillation in $x$, avoiding the use of normalized adjoint solutions required in previous works. |
| title | Two-sided Gaussian estimates for fundamental solutions of second-order parabolic equations in non-divergence form |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.12659 |