Brenier-Schrödinger problem on compact manifold with boundary
Résumé
We consider the Brenier-Schrödinger problem on compact manifolds with boundary. In the spirit of a work by Arnaudon, Cruzeiro, Léonard 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.
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