Brenier-Schr{ö}dinger problem on compact manifold with boundary
arXiv:2102.07410
Abstract
We consider the Brenier-Schr{ö}dinger problem on compact manifolds with boundary. In the spirit of a work by Arnaudon, Cruzeiro, L{é}onard and Zambrini, we study the kinetic property of regular solutions and obtain a link to the Navier-Stokes equations with an impermeability condition. We also enhance the class of models for which the problem admits a unique solution. This involves a method of taking quotients by reflection groups for which we give several examples.
26 pages