Necessary and sufficient conditions for discrete and differential inclusions of elliptic type

E. N. Mahmudov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

51 Citations (Scopus)

Abstract

This paper deals for the first time with the Dirichlet problem for discrete (PD), discrete approximation problem on a uniform grid and differential (PC) inclusions of elliptic type. In the form of Euler-Lagrange inclusion necessary and sufficient conditions for optimality are derived for the problems under consideration on the basis of new concepts of locally adjoint mappings. The results obtained are generalized to the multidimensional case with a second order elliptic operator.

Original languageEnglish
Pages (from-to)768-789
Number of pages22
JournalJournal of Mathematical Analysis and Applications
Volume323
Issue number2
DOIs
Publication statusPublished - 15 Nov 2006
Externally publishedYes

Keywords

  • Dirichlet problems
  • Discrete and differential inclusion
  • Discrete approximation
  • Locally adjoint mappings
  • Necessary and sufficient conditions
  • Nonsmooth analysis

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