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On the Regularity of an Obstacle Control Problem

✍ Scribed by Hongwei Lou

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
145 KB
Volume
258
Category
Article
ISSN
0022-247X

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✦ Synopsis

An optimal control problem of the obstacle for an elliptic variational inequality is considered, in which the obstacle is regarded as the control. To get the regularity of the optimal pair, a new related control problem is introduced. By proving the existence of an optimal pair to such a new control problem, the regularity of the optimal pair to the original problem is obtained. It turns out that the regularity obtained is sharp in general. Some other interesting properties of the optimal pair are also established.

πŸ“œ SIMILAR VOLUMES

Continuous dependence of the scattering
Continuous dependence of the scattering amplitude on the surface of an obstacle
✍ A. G. Ramm πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 280 KB

## Abstract Let __D~j~__,__j__ = 1,2, be two bounded domains (obstacles) in ℝ^__n__^, __n__ β‰₯ 2, with the boundaries Ξ“~__j__~. Let __A~j~__ be the scattering amplitude corresponding to __D~j~__. The Dirichlet boundary condition is assumed on Ξ“~__j__~. A formula is derived for __A__:= __A__~1~ βˆ’ __A