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Kinetic maximal $$L^2$$ L 2 -regularity for the (fractional) Kolmogorov equation
Journal of Evolution Equations ( IF 1.1 ) Pub Date : 2021-04-08 , DOI: 10.1007/s00028-021-00669-3
Lukas Niebel , Rico Zacher

We introduce the notion of kinetic maximal \(L^2\)-regularity with temporal weights for the (fractional) Kolmogorov equation. In particular, we determine the function spaces for the inhomogeneity and the initial value which characterize the regularity of solutions to the fractional Kolmogorov equation in terms of fractional anisotropic Sobolev spaces. It is shown that solutions of the homogeneous (fractional) Kolmogorov equation define a semi-flow in a suitable function space and the property of instantaneous regularization is investigated.



中文翻译:

(分数)Kolmogorov方程的动力学最大$$ L ^ 2 $$ L 2-正则性

对于(分数)Kolmogorov方程,我们引入了具有时间权重的动力学最大值\(L ^ 2 \) -正则性的概念。特别是,我们确定了不均匀性的函数空间和初始值,这些函数空间以分数各向异性Sobolev空间为特征,描述了分数Kolmogorov方程解的正则性。结果表明,齐次(分数阶)Kolmogorov方程的解在适当的函数空间中定义了半流,并研究了瞬时正则化的性质。

更新日期:2021-04-09
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