论文标题
Sobolev嵌入动力学Fokker-Planck方程
Sobolev embeddings for kinetic Fokker-Planck equations
论文作者
论文摘要
我们引入了一类超伴侣的kolmogorov型操作员，介绍了可满足弱的Hörmander条件的一类sobolev-slobodeckij空间。我们证明连续嵌入洛伦兹和内在的霍尔德空间中。我们还通过固有的泰勒膨胀证明了近似和插值不平等，从而扩展了Hölder空间的类似结果。一阶的嵌入是通过通过Luc Tartar调整方法来证明的，该方法仅利用固有的准标准的缩放特性，而对于较高的阶，我们使用统一的内核估计值。
We introduce intrinsic Sobolev-Slobodeckij spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak Hörmander condition. We prove continuous embeddings into Lorentz and intrinsic Hölder spaces. We also prove approximation and interpolation inequalities by means of an intrinsic Taylor expansion, extending analogous results for Hölder spaces. The embedding at first order is proved by adapting a method by Luc Tartar which only exploits scaling properties of the intrinsic quasi-norm, while for higher orders we use uniform kernel estimates.
