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Regularity theory of Kolmogorov operator revisited
Canadian Mathematical Bulletin ( IF 0.5 ) Pub Date : 2020-08-24 , DOI: 10.4153/s0008439520000697 Damir Kinzebulatov
中文翻译:
重新审视 Kolmogorov 算子的正则性理论
更新日期:2020-08-24
Canadian Mathematical Bulletin ( IF 0.5 ) Pub Date : 2020-08-24 , DOI: 10.4153/s0008439520000697 Damir Kinzebulatov
We consider Kolmorogov operator $-\Delta +b \cdot \nabla $ with drift b in the class of form-bounded vector fields (containing vector fields having critical-order singularities). We characterize quantitative dependence of the Sobolev and Hölder regularity of solutions to the corresponding elliptic equation on the value of the form-bound of b.
中文翻译:
重新审视 Kolmogorov 算子的正则性理论
我们考虑 Kolmorogov 算子 $-\Delta +b \cdot \nabla $, 其中漂移b属于形式有界向量场(包含具有临界阶奇点的向量场)。我们描述了相应椭圆方程解的 Sobolev 和 Hölder 正则性对b的形式边界值的定量依赖性。