Abstract
Under the bounded geometry assumption on Riemannian manifold M, a variational approximation for Fokker-Planck equation on M is constructed by the scheme of Jordan et al. in SIAM J Math Anal 29(1):1-17, 1998. Moreover, the uniqueness and global L p -estimate of the solution for 1 < p < dim(M)/(dim(M) - 1) are obtained for a broad class of potential.
| Original language | English |
|---|---|
| Pages (from-to) | 519-539 |
| Number of pages | 21 |
| Journal | Probability Theory and Related Fields |
| Volume | 137 |
| Issue number | 3-4 |
| DOIs | |
| Publication status | Published - Mar 2007 |
| Externally published | Yes |
Keywords
- Fokker-Planck equation
- Free energy
- Gradient flow
- Heat kernel
- Wasserstein metric