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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.07341 |
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| _version_ | 1866911369013493760 |
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| author | Frank, Rupert L. Larson, Simon |
| author_facet | Frank, Rupert L. Larson, Simon |
| contents | We prove a bound on the heat trace of the Neumann Laplacian on a convex domain that captures the first two terms in its small-time expansion, but is valid for all times and depends on the underlying domain only through very simple geometric characteristics. This is proved via a precise and uniform expansion of the on-diagonal heat kernel close to the boundary. Most of our results are valid without the convexity assumption and we also consider two-term asymptotics for the heat trace for Lipschitz domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07341 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniform bounds for Neumann heat kernels and their traces in convex sets Frank, Rupert L. Larson, Simon Analysis of PDEs Spectral Theory We prove a bound on the heat trace of the Neumann Laplacian on a convex domain that captures the first two terms in its small-time expansion, but is valid for all times and depends on the underlying domain only through very simple geometric characteristics. This is proved via a precise and uniform expansion of the on-diagonal heat kernel close to the boundary. Most of our results are valid without the convexity assumption and we also consider two-term asymptotics for the heat trace for Lipschitz domains. |
| title | Uniform bounds for Neumann heat kernels and their traces in convex sets |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2601.07341 |