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Title: Abstract theory of variational inequalities with Lagrange multipliers and application to nonlinear PDEs (English)
Author: Fukao, Takeshi
Author: Kenmochi, Nobuyuki
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 139
Issue: 2
Year: 2014
Pages: 391-399
Summary lang: English
Category: math
Summary: Recently, we established some generalizations of the theory of Lagrange multipliers arising from nonlinear programming in Banach spaces, which enable us to treat not only elliptic problems but also parabolic problems in the same generalized framework. The main objective of the present paper is to discuss a typical time-dependent double obstacle problem as a new application of the above mentioned generalization. Actually, we describe it as a usual parabolic variational inequality and then characterize it as a parabolic inclusion by using the Lagrange multiplier and the nonlinear maximal monotone operator associated with the time differential under time-dependent double obstacles. (English)
Keyword: Lagrange multiplier
Keyword: parabolic variational inequality
MSC: 34G25
MSC: 35K86
MSC: 35R20
MSC: 47J20
idZBL: Zbl 06362268
idMR: MR3238849
DOI: 10.21136/MB.2014.143864
Date available: 2014-07-14T08:44:56Z
Last updated: 2020-07-29
Stable URL:
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