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HARNACK-TYPE INEQUALITIES FOR THE POROUS MEDIUM EQUATION ON A MANIFOLD WITH NON-NEGATIVE RICCI CURVATURE
- Authors
- Chang, Jeongwook; Lee, Jinho
- Issue Date
- Apr-2012
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Keywords
- Porous medium equation; Harnack inequality; geodesic; Ricci curvature
- Citation
- INTERNATIONAL JOURNAL OF MATHEMATICS, v.23, no.4
- Journal Title
- INTERNATIONAL JOURNAL OF MATHEMATICS
- Volume
- 23
- Number
- 4
- ISSN
- 0129-167X
1793-6519
- Abstract
- We derive Harnack-type inequalities for non-negative solutions of the porous medium equation on a complete Riemannian manifold with non-negative Ricci curvature. Along with gradient estimates, reparametrization of a geodesic and time rescaling of a solution are key tools to get the results.
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