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Title: Directional differentiability for elliptic quasi-variational inequalities of obstacle type
Authors: Alphonse, AmalHintermüller, MichaelRautenberg, Carlos N.
Publishers Version: https://doi.org/10.20347/WIAS.PREPRINT.2492
Issue Date: 2018
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2492, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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: Quasi-variational inequality; obstacle problem; state constraint; conical derivative; directional differentiability; thermoforming
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik



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