Adding a Sobolev (H1) regularization to quantile-function gradient flows guarantees existence of generalized minimizing movements for positive distance-kernel MMD and rectifies a mass-dissipation defect for the negative kernel.
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Wasserstein Gradient Flows of MMD Functionals with Distance Kernels under Sobolev Regularization
Adding a Sobolev (H1) regularization to quantile-function gradient flows guarantees existence of generalized minimizing movements for positive distance-kernel MMD and rectifies a mass-dissipation defect for the negative kernel.