Maximal regularity for the Cauchy problem of the heat equation?in <i>BMO</i>
Maximal regularity for the Cauchy problem of the heat equation?in <i>BMO</i>
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<i>BMO</i> 中热方程柯西问题的最大正则性？
DOI：
10.1002/mana.201900506
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发表时间：
2022
影响因子：
1
通讯作者：
Shimizu Senjo
中科院分区：
文献类型：
--
作者：
Ogawa Takayoshi;Shimizu Senjo
考虑一类有界平均振荡（BMO$BMO$）中热方程Cauchy问题的极大正则性。非自反Banach空间的极大正则性不是由已有的抽象理论得到的。基于BMO$BMO$‐表达式的对称性质，我们得到了BMO$BMO$中热方程的极大正则性及其锐迹估计。结果表明，Stein[50]和Koch-Tataru[32]得到的齐次初始估计可以增强到对外力的非齐次估计，所得到的估计可以适用于拟线性问题。我们的方法基于分部积分法，也适用于其他类型的抛物型问题。
We consider maximal regularity for the Cauchy problem of the heat equation in a class of bounded mean oscillations (BMO$BMO$). Maximal regularity for non‐reflexive Banach spaces is not obtained by the established abstract theory. Based on the symmetric characterization of BMO$BMO$‐expression, we obtain maximal regularity for the heat equation in BMO$BMO$ and its sharp trace estimate. Our result shows that the homogeneous initial estimate obtained by Stein [50] and Koch–Tataru [32] can be strengthened up to the inhomogeneous estimate for the external forces and the obtained estimates can be applicable to quasilinear problems. Our method is based on integration by parts and can also be applicable to other type of parabolic problems.