Reflected diffusion, no-flux continuity equations and confined Lagrangian flows in bounded domains
Motivated by marginal distribution flows of reflected diffusions in bounded domains, we investigate when a density/flux pair solving a no-flux continuity equation admits a regular Lagrangian flow that remains in the closed domain and generates the prescribed density flow. We give sufficient conditions in terms of interior bounded-variation regularity, bounded-variation control on a boundary collar, a one-sided bound on an absolutely continuous divergence, and vanishing normal trace of the velocity. The proof uses the fact that tangency removes the singular boundary contribution to the divergence of the zero extension, thereby making the extended velocity admissible for the Ambrosio-DiPern...
| Authors | Rama Cont |
|---|---|
| Primary category | math.CA |
| Published | 30 July 2026 |
| Last updated at source | 30 July 2026 |
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