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 language | English |
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Pages (from-to) | 768-789 |
Number of pages | 22 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 323 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Nov 2006 |
Externally published | Yes |
Keywords
- Dirichlet problems
- Discrete and differential inclusion
- Discrete approximation
- Locally adjoint mappings
- Necessary and sufficient conditions
- Nonsmooth analysis