Geodesic
Abstract theory of variational inequalities with Lagrange multipliers and application to nonlinear PDEs
Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 391-399

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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.
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.
DOI : 10.21136/MB.2014.143864
Classification : 34G25, 35K86, 35R20, 47J20
Keywords: Lagrange multiplier; parabolic variational inequality 
Fukao, Takeshi; Kenmochi, Nobuyuki. Abstract theory of variational inequalities with Lagrange multipliers and application to nonlinear PDEs. Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 391-399. doi: 10.21136/MB.2014.143864
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