Directional differentiability for elliptic quasi-variational inequalities of obstacle type
Abstract
The directional differentiability of the solution map of obstacle type quasi-variational inequalities (QVIs) with respect to perturbations on the forcing term is studied. The classical result of Mignot is then extended to the quasi-variational case under assumptions that allow multiple solutions of the QVI. The proof involves selection procedures for the solution set and represents the directional derivative as the limit of a monotonic sequence of directional derivatives associated to specific variational inequalities. Additionally, estimates on the coincidence set and several simplifications under higher regularity are studied. The theory is illustrated by a detailed study of an application to thermoforming comprising of modelling, analysis and some numerical experiments.
Keywords
Cite
@article{arxiv.1802.03564,
title = {Directional differentiability for elliptic quasi-variational inequalities of obstacle type},
author = {Amal Alphonse and Michael Hintermüller and Carlos N. Rautenberg},
journal= {arXiv preprint arXiv:1802.03564},
year = {2019}
}
Comments
This version has a revised assumption (A5) which is less restrictive than before