论文标题
非线性fokker-planck方程，带有分数拉普拉斯和麦基恩·弗拉索夫sdes和lévy-noise
Nonlinear Fokker-Planck equations with fractional Laplacian and McKean-Vlasov SDEs with Lévy-Noise
论文作者
论文摘要
这项工作与具有分数拉普拉斯操作员$（ - δ）^s $的非线性fokker-planck方程存在温和的解决方案有关，in \ weft（\ frac12,1 \ right）$。 Schwartz分布解决方案的唯一性也被证明是在扩散和漂移项的适当假设下证明。作为应用程序，对McKean-Vlasov方程的解决方案薄弱和具有Lévy-Noise的唯一性以及其法律的Markov财产。
This work is concerned with the existence of mild solutions to non-linear Fokker-Planck equations with fractional Laplace operator $(-Δ)^s$ for $s\in\left(\frac12,1\right)$. The uniqueness of Schwartz distributional solutions is also proved under suitable assumptions on diffusion and drift terms. As applications, weak existence and uniqueness of solutions to McKean-Vlasov equations with Lévy-Noise, as well as the Markov property for their laws are proved.
