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.Farshbaf Shaker, Mohammad HassanFukao, TakeshiYamazaki, Noriaki2016-03-242019-06-282014https://doi.org/10.34657/3188https://oa.tib.eu/renate/handle/123456789/2939We consider the Allen-Cahn equation with constraint. Our constraint is the subdifferential of the indicator function on the closed interval, which is the multivalued function. In this paper we give the characterization of the Lagrange multiplier to our equation. Moreover, we consider the singular limit of our system and clarify the limit of the solution and the Lagrange multiplier to our problem.application/pdfeng510Allen-Cahn equationconstraintdouble obstaclesingular limitLagrange multipliersubdifferentialReport