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

[摘要] This paper deals for the first time with the Dirichlet problem for discrete (P-D), discrete approximation problem on a uniform grid and differential (P-C) 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. (c) 2005 Published by Elsevier Inc.

[发布日期] 2006-11-15

[关键词] discrete approximation;discrete and differential inclusion;Dirichlet problems;nonsmooth analysis;locally adjoint mappings;necessary and sufficient conditions