Article citationsMore>>

E. N. Mahmudov, “Necessary and Sufficient Conditions for Discrete and Differential Inclusions of Elliptic Type,” Journal of Mathematical Analysis and Applications, Vol. 323, No. 2, 2006, pp. 768-789. doi:10.1016/j.jmaa.2005.10.069

has been cited by the following article:

• TITLE: Sufficient Conditions of Optimality for Convex Differential Inclusions of Elliptic Type and Duality

  AUTHORS: Elimhan N. Mahmudov

  KEYWORDS: Differential Inclusion; Dirichlet; Locally Adjoint; Sufficient Conditions; Duality

  JOURNAL NAME: Advances in Pure Mathematics, Vol.2 No.2, March 22, 2012

  ABSTRACT: 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 proved. The results obtained are generalized to the multidimensional case with a second order elliptic operator.