Abstract
We prove a formula representing solutions to parabolic Fokker–Planck–Kolmogorov equations with coefficients of low regularity. This formula is applied for proving the continuity of solution densities under broad assumptions and obtaining upper bounds for them. In the case of diffusion coefficients of class VMO\(_x\), we show that the solution density is locally integrable to any power.
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Acknowledgements
This research was supported by the RFBR Grants 17-01-00662 and 18-31-20008 and the DFG through the project RO 1195/12-1 and the CRC 1283 at Bielefeld University. We are very grateful to the anonymous referee for important corrections and useful remarks taken into account in the final version.
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Bogachev, V.I., Shaposhnikov, S.V. Representations of solutions to Fokker–Planck–Kolmogorov equations with coefficients of low regularity. J. Evol. Equ. 20, 355–374 (2020). https://doi.org/10.1007/s00028-019-00532-6
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DOI: https://doi.org/10.1007/s00028-019-00532-6