Evolutionary quasi-variational and variational inequalities with constraints on the derivatives

Abstract: This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination of partial derivatives of the solutions. The quasi-linear operators are of monotone type, but are not required to be coercive for the existence of weak solutions, which is obtained by a double penalization/regularization for the approximation of the solutions. In the case of time-dependent convex sets that are independent of the solution, we show also the uniqueness and the continuous dependence of the strong solutions of the variational inequalities, extending previous results to a more general framework.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Evolutionary quasi-variational and variational inequalities with constraints on the derivatives ; volume:9 ; number:1 ; year:2018 ; pages:250-277 ; extent:28 ; Advances in nonlinear analysis ; 9, Heft 1 (2018), 250-277 (gesamt 28)

Contributors, Places and Time

• Creator: Miranda, Fernando ; Rodrigues, José Francisco ; Santos, Lisa

Further information

• DOI: 10.1515/anona-2018-0113
• URN: urn:nbn:de:101:1-2405021553456.486341701343
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 10:59 AM CEST