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.

中文翻译：

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具有低正则系数的Fokker-Planck-Kolmogorov方程的解的表示

我们证明了一个方程，该方程表示具有低正则系数的抛物型Fokker-Planck-Kolmogorov方程的解。该公式适用于证明在宽泛的假设下溶液密度的连续性，并为它们确定上限。在VMO \（_ x \）类的扩散系数的情况下，我们证明了解密度对于任何幂都是局部可积分的。