Curvature conditions, Liouville-type theorems and Harnack inequalities for a nonlinear parabolic equation on smooth metric measure spaces
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| Format: | Preprint |
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2024
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| _version_ | 1866911824068214784 |
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| author | Taheri, Ali Vahidifar, Vahideh |
| author_facet | Taheri, Ali Vahidifar, Vahideh |
| contents | In this paper we prove gradient estimates of both elliptic and parabolic types, specifically, of Souplet-Zhang, Hamilton and Li-Yau types for positive smooth solutions to a class of nonlinear parabolic equations involving the Witten or drifting Laplacian on smooth metric measure spaces. These estimates are established under various curvature conditions and lower bounds on the generalised Bakry-Émery Ricci tensor and find utility in proving elliptic and parabolic Harnack-type inequalities as well as general elliptic and parabolic Liouville-type and other global constancy results. Several applications and consequences are presented and discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_01749 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curvature conditions, Liouville-type theorems and Harnack inequalities for a nonlinear parabolic equation on smooth metric measure spaces Taheri, Ali Vahidifar, Vahideh Analysis of PDEs In this paper we prove gradient estimates of both elliptic and parabolic types, specifically, of Souplet-Zhang, Hamilton and Li-Yau types for positive smooth solutions to a class of nonlinear parabolic equations involving the Witten or drifting Laplacian on smooth metric measure spaces. These estimates are established under various curvature conditions and lower bounds on the generalised Bakry-Émery Ricci tensor and find utility in proving elliptic and parabolic Harnack-type inequalities as well as general elliptic and parabolic Liouville-type and other global constancy results. Several applications and consequences are presented and discussed. |
| title | Curvature conditions, Liouville-type theorems and Harnack inequalities for a nonlinear parabolic equation on smooth metric measure spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.01749 |