Abstract

A family of maximally monotone operators on a separable Hilbert space is considered. The domains of these operators depend on time ranging over an interval of the real line. The space of square-integrable functions on this interval taking values in the same Hilbert space is also considered. On the space of square-integrable functions a superposition (Nemytskii) operator is constructed based on a family of maximally monotone operators. Under fairly general assumptions, the maximal monotonicity of the Nemytskii operator is proved. This result is applied to the family of maximally monotone operators endowed with a pseudodistance in the sense of A. A. Vladimirov, to the family of subdifferential operators generated by a proper convex lower semicontinuous function depending on time, and to the family of normal cones of a moving closed convex set.

中文翻译：

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Nemytskii 算子的最大单调性

摘要

考虑可分离希尔伯特空间上的最大单调算子族。这些算子的域取决于实线间隔上的时间范围。还考虑了在同一 Hilbert 空间中取值的该区间上的平方可积函数空间。在平方可积函数空间上，一个叠加（Nemytskii）算子是基于一组最大单调算子构建的。在相当一般的假设下，证明了 Nemytskii 算子的最大单调性。该结果适用于具有 AA Vladimirov 意义上的伪距离的最大单调算子族，适用于由适当的凸下半连续函数随时间生成的次微分算子族，以及运动的法向锥族闭凸集。