An approach for weighted mixed-norm estimates for parabolic equations with local and non-local time derivatives
An approach for weighted mixed-norm estimates for parabolic equations with local and non-local time derivatives
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DOI：
10.1016/j.aim.2020.107494
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发表时间：
2020-03
影响因子：
1.7
通讯作者：
Hongjie Dong;Doyoon Kim
中科院分区：
文献类型：
--
作者：
Hongjie Dong;Doyoon Kim
本文给出了通常抛物型方程和时间分数抛物型方程在系数仅在时间变量上可测时的加权混合范数估计和可解性的统一方法。在空间变量中，前导系数局部具有较小的平均振荡。我们的结果扩展了[5]中之前的结果，用于没有权重的未混合L - p估计。
We give a unified approach to weighted mixed-norm estimates and solvability for both the usual and time fractional parabolic equations in nondivergence form when coefficients are merely measurable in the time variable. In the spatial variables, the leading coefficients locally have small mean oscillations. Our results extend the previous result in [5] for unmixed L p-estimates without weights.