Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators

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Limit theorems for some branching measure-valued processes (2011, background): “) As illustrated in [15] for instance, the question of uniqueness for evolution equations is generally nontrivial.”
Mosco convergence of Dirichlet forms in infinite dimensions with changing reference measures (2006, background): “Some partial results on convergence of semigroups and processes in the infinite-dimensional case have been obtained in [12,21,22,36].”
Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces (2012, methodology): “It is shown below that for local Dirichlet forms this approach may be seen as an extension of closely related and preceding constructions of Eberle, [16], based on abstract (local) differential operators.”
Particle approximation of the Wasserstein diffusion (2007, background): “The verification is usually difficult, in particular in a non-Gaussian infinite dimensional setting involving singular logarithmic derivatives [6].”