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arXiv · 1802.03564

Directional differentiability for elliptic quasi-variational inequalities of obstacle type

Amal Alphonse·Michael Hintermüller·Carlos N. Rautenberg
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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.

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Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg. 2019-11-27. Directional differentiability for elliptic quasi-variational inequalities of obstacle type. https://arxiv.org/abs/1802.03564

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