Elliptic and parabolic equations for measures

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On large deviations of coupled diffusions with time scale separation (2013, background): “(7.26) By (7.13a), Theorem 5.5.5′(a) on page 156 in Morrey [32], the discussion on page 12 of Bogachev, Krylov and Rëkner [7], Shaposhnikov [47] and the fact that supx∈S̆ |as(u, x)| and ‖cs(u, ·)‖W1,∞(S̆,Rl×l ) are bounded locally uniformly in (s, u), we have that ‖ws(u, ·)‖W1,q (S̃) ≤ MS̃,S̆,q(1 + ”
Distances between transition probabilities of diffusions and applications to nonlinear Fokker–Planck–Kolmogorov equations (2016, background): “It is known (see [7] or [8]) that the measure μ possesses a continuous positive density % on Rd × (0, T ) with respect to Lebesgue measure, moreover, for each ball U in Rd, for almost every t ∈ (0, T ) one has %( · , t) ∈ W p,1(U) for all p ∈ [1,+∞) and the function ‖%( · , t)‖pLp(U) + ‖∇%( · , t)‖p”
Ergodicity of stochastic differential equations with jumps and singular coefficients (2017, background): “11) are also studied in [5, 6, 10], see also [46].”
Steady States of Fokker–Planck Equations: I. Existence (2015, background): “Let U be a C2 compact function in U with essential upper bound ρM .”