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Duality Problems in the Convex Differential Inclusions of Elliptic Type

Year 2010, Volume: 3 , 161 - 170, 23.10.2010

Abstract

This paper deals with the Dirichlet problem for convex differential (PC) inclusions of elliptic type. On the basis of Legendre-Fenchel transforms 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 proved. The results obtained are generalized to the multidimensional case with a second order elliptic operator.

Duality Problems in the Convex Differential Inclusions of Elliptic Type

Year 2010, Volume: 3 , 161 - 170, 23.10.2010

Abstract

This paper deals with the Dirichlet problem for convex differential (PC) inclusions of elliptic type. On the basis of Legendre-Fenchel transforms 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 proved. The results obtained are generalized to the multidimensional case with a second order elliptic operator. 

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Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Elimhan Mahmudov

Publication Date October 23, 2010
Published in Issue Year 2010 Volume: 3

Cite

APA Mahmudov, E. (2010). Duality Problems in the Convex Differential Inclusions of Elliptic Type. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy, 3, 161-170.
AMA Mahmudov E. Duality Problems in the Convex Differential Inclusions of Elliptic Type. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy. October 2010;3:161-170.
Chicago Mahmudov, Elimhan. “Duality Problems in the Convex Differential Inclusions of Elliptic Type”. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy 3, October (October 2010): 161-70.
EndNote Mahmudov E (October 1, 2010) Duality Problems in the Convex Differential Inclusions of Elliptic Type. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy 3 161–170.
IEEE E. Mahmudov, “Duality Problems in the Convex Differential Inclusions of Elliptic Type”, İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy, vol. 3, pp. 161–170, 2010.
ISNAD Mahmudov, Elimhan. “Duality Problems in the Convex Differential Inclusions of Elliptic Type”. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy 3 (October 2010), 161-170.
JAMA Mahmudov E. Duality Problems in the Convex Differential Inclusions of Elliptic Type. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy. 2010;3:161–170.
MLA Mahmudov, Elimhan. “Duality Problems in the Convex Differential Inclusions of Elliptic Type”. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy, vol. 3, 2010, pp. 161-70.
Vancouver Mahmudov E. Duality Problems in the Convex Differential Inclusions of Elliptic Type. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy. 2010;3:161-70.