Back to Search
Start Over
Curvature conditions, Liouville-type theorems and Harnack inequalities for a nonlinear parabolic equation on smooth metric measure spaces
- Source :
- Advanced Nonlinear Studies, Vol 24, Iss 3, Pp 553-591 (2024)
- Publication Year :
- 2024
- Publisher :
- De Gruyter, 2024.
-
Abstract
- 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 Liouville-type and other global constancy results. Several applications and consequences are presented and discussed.
Details
- Language :
- English
- ISSN :
- 21690375
- Volume :
- 24
- Issue :
- 3
- Database :
- Directory of Open Access Journals
- Journal :
- Advanced Nonlinear Studies
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.905a9020d134bcba225182c134154c4
- Document Type :
- article
- Full Text :
- https://doi.org/10.1515/ans-2023-0120