A gradient flow that is none: Heat flow with Wentzell boundary condition
Analysis of PDEs
2025-06-30 v1 Probability
Abstract
We establish a representation of the heat flow with Wentzell boundary conditions on smooth domains as gradient descent dynamics for the entropy in a suitably extended Otto manifold of probability measures with additional boundary parts. Yet it is shown that for weak boundary diffusion, the associated Fokker-Planck dynamics cannot be recovered from any entropy-driven metric JKO-Wasserstein scheme, at least if the underlying point metric satisfies certain natural regularity assumptions. This discrepancy is illustrated in competing large-deviation heuristics in the Sanov and Schilder regimes.
Cite
@article{arxiv.2506.22093,
title = {A gradient flow that is none: Heat flow with Wentzell boundary condition},
author = {Marie Bormann and Léonard Monsaingeon and D. R. Michiel Renger and Max von Renesse},
journal= {arXiv preprint arXiv:2506.22093},
year = {2025}
}