The talk aims to present two ideas, useful for proving the existence of solutions for fourth-order Cahn-Hilliard PDEs, with JKO-type schemes. The first idea is to use a scheme with weighted Wasserstein distance, if the equation has a general concave mobility m(u), instead of the usual m(u)=u which leads to the usual Wasserstein distance. These distances were introduced in Dolbeault, Nazaret, Savaré, CalcVar 2009. The second idea is the flow interchange lemma, which allows to compute the dissipation of an entropy along the iterations of the JKO scheme. This lemma was applied in Lisini, Matthes, Savaré, JDE 2012.
