Optimization of elliptic type differential inclusions and duality

This paper deals with the Dirichlet problem for convex differential (PC) inclusions of elliptic type. On the basis of conjugacy correspondence the dual problems are constructed. Using the new concepts of locally adjoint mappings in the form of Euler-Lagrange type inclusion is established extremal re...

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Bibliographic Details
Published in:TWMS journal of applied and engineering mathematics 2012-01, Vol.2 (1), p.60-66
Main Author: Mahmudov, E.N
Format: Article
Language:English
Subjects:
Adjoints
Convex functions
Differential equations
Dirichlet problem
Duality theorem
Duality theory (Mathematics)
Inclusions
Mapping
Mathematical analysis
Mathematical research
Operators
Optimization
Partial differential equations
Series, Dirichlet
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Summary:This paper deals with the Dirichlet problem for convex differential (PC) inclusions of elliptic type. On the basis of conjugacy correspondence the dual problems are constructed. Using the new concepts of locally adjoint mappings in the form of Euler-Lagrange type inclusion is established extremal relations for primary and dual problems. Then duality problems are formulated for convex problems and duality theorems are proven. The results obtained are generalized to the multidimensional case with a second order elliptic operator.
ISSN:2146-1147
2146-1147