A gradient flow that is none: Heat flow with Wentzell boundary conditions

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 we show 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. The talk is based on joint work with Léonard Monsaingeon, Michiel Renger and Max von Renesse.