On the differentiability of the minimal and maximal solution maps of elliptic quasi-variational inequalities
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Publication:2247706
DOI10.1016/J.JMAA.2021.125732zbMATH Open1477.49011arXiv2009.01626OpenAlexW3206387853MaRDI QIDQ2247706
Author name not available (Why is that?)
Publication date: 17 November 2021
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/2009.01626
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