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تسجيل مستخدم جديدOn $L^1$-estimates for probability solutions to Fokker-Planck-Kolmogorov equations
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We prove two new results connected with elliptic Fokker-Planck-Kolmogorov equations with drifts integrable with respect to solutions. The first result answers negatively a long-standing question and shows that a density of a probability measure satisfying the Fokker-Planck-Kolmogorov equation with a drift integrable with respect to this density can fail to belong to the Sobolev class~$W^{1,1}(mathbb{R}^d)$. There is also a version of this result for densities with respect to Gaussian measures. The second new result gives some positive information about properties of such solutions: the solution density is proved to belong to certain fractional Sobolev classes.
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