On the differentiability of the minimal and maximal solution maps of elliptic quasi-variational inequalities

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...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2021-10
Main Authors: Amal Alphonse, Hintermüller, Michael, Rautenberg, Carlos N
Format: Article
Language:English
Subjects:
Derivatives
Estimates
Inequalities
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2009.01626