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arXiv 1601.08012math.FAmath.AP
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J. - L.关于非自治形式控制方程的极大正则性的Lions问题

J.-L. Lions' Problem Concerning Maximal Regularity of Equations Governed by Non-Autonomous Forms

Stephan Fackler

摘要:

一个老问题,由于J。L.狮子回到20世纪60年代问抽象柯西问题相关的非自治形式是否有最大的规律性,如果时间依赖性只是假设是连续的,甚至是可测量的。我们给出了一个否定的回答这个问题,并讨论了积极的结果所需的最小正则性。

英文摘要:

An old problem due to J.-L. Lions going back to the 1960s asks whether the abstract Cauchy problem associated to non-autonomous forms has maximal regularity if the time dependence is merely assumed to be continuous or even measurable. We give a negative answer to this question and discuss the minimal regularity needed for positive results.

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