On the differentiability of the minimal and maximal solution maps of elliptic quasi-variational inequalities
On the differentiability of the minimal and maximal solution maps of elliptic quasi-variational inequalities
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DOI：
10.1016/j.jmaa.2021.125732
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发表时间：
2020-09
影响因子：
1.3
通讯作者：
A. Alphonse;M. Hintermüller;C. N. Rautenberg
中科院分区：
文献类型：
--
作者：
A. Alphonse;M. Hintermüller;C. N. Rautenberg
本文证明了障碍型椭圆拟变分不等式的最小解映射和最大解映射关于强迫项和有符号的方向是方向可微的。沿着的方式，我们表明，最小和最大的解决方案可以被看作是单调极限的某些变分不等式的解决方案，上述方向导数也可以被表征为单调极限的序列的方向导数相关的变分不等式。最后，我们总结了一些例子和热成型的应用。
In this note, we prove that the minimal and maximal solution maps associated to elliptic quasi-variational inequalities of obstacle type are directionally differentiable with respect to the forcing term and for directions that are signed. Along the way, we show that the minimal and maximal solutions can be seen as monotone limits of solutions of certain variational inequalities and that the aforementioned directional derivatives can also be characterised as the monotone limits of sequences of directional derivatives associated to variational inequalities. We conclude the paper with some examples and an application to thermoforming.