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First essential m-dissipativity of an infinite-dimensional Ornstein-Uhlenbeckoperator $N$, perturbed by the gradient of a potential, on a domain$\mathcal{F}C_b^{\infty}$ of finitely based, smooth and bounded functions, isshown. Our considerations allow unbounded diffusion operators as coefficients.We derive corresponding second order regularity estimates for solutions $f$ ofthe Kolmogorov equation $\alpha f-Nf=g$, $\alpha \in (0,\infty)$, generalizingsome results of Da Prato and Lunardi. Second we prove essential m-dissipativityfor generators $(L_{\Phi},\mathcal{F}C_b^{\infty})$ of infinite-dimensionalnon-linear degenerate diffusion processes. We emphasize that the essentialm-dissipativity of $(L_{\Phi},\mathcal{F}C_b^{\infty})$ is useful to applygeneral resolvent methods developed by Beznea, Boboc and R\"ockner, in order toconstruct martingale/weak solutions to infinite-dimensional non-lineardegenerate diffusion equations. Furthermore, the essential m-dissipativity of$(L_{\Phi},\mathcal{F}C_b^{\infty})$ and $(N,\mathcal{F}C_b^{\infty})$, as wellas the regularity estimates are essential to apply the general abstract Hilbertspace hypocoercivity method from Dolbeault, Mouhot, Schmeiser and Grothaus,Stilgenbauer, respectively, to the corresponding diffusions.

Essential m-dissipativity for generators of infinite-dimensional non-linear degenerate diffusion processes