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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/2505.07565 |
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| _version_ | 1866909607739260928 |
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| author | Hu, Yuanyang |
| author_facet | Hu, Yuanyang |
| contents | Let $G=(V, E)$ be a locally finite connected graph satisfying curvature-dimension conditions ($CDE(n, 0)$ or its strengthened version $CDE'(n, 0))$) and polynomial volume growth conditions of degree $m$. We systematically establish sharp $L^{p}$-bounds and decay-type $L^{p}$-$L^{q}$ estimates for heat operators on $G$, accommodating both bounded and unbounded Laplacians. The analysis utilizes Li-Yau-type Harnack inequalities and geometric completeness arguments to handle degenerate cases. As a key application, we prove the existence of global solutions to a semilinear parabolic system on $G$ under critical exponents governed by volume growth dimension $m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07565 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $L^{p}$-$L^{q}$ estimates of the heat kernels on graphs with applications to a parabolic system Hu, Yuanyang Analysis of PDEs Let $G=(V, E)$ be a locally finite connected graph satisfying curvature-dimension conditions ($CDE(n, 0)$ or its strengthened version $CDE'(n, 0))$) and polynomial volume growth conditions of degree $m$. We systematically establish sharp $L^{p}$-bounds and decay-type $L^{p}$-$L^{q}$ estimates for heat operators on $G$, accommodating both bounded and unbounded Laplacians. The analysis utilizes Li-Yau-type Harnack inequalities and geometric completeness arguments to handle degenerate cases. As a key application, we prove the existence of global solutions to a semilinear parabolic system on $G$ under critical exponents governed by volume growth dimension $m$. |
| title | $L^{p}$-$L^{q}$ estimates of the heat kernels on graphs with applications to a parabolic system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.07565 |