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An Existence Result for Optimal Obstacles

✍ Scribed by Dorin Bucur; Giuseppe Buttazzo; Paola Trebeschi

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
209 KB
Volume
162
Category
Article
ISSN
0022-1236

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✦ Synopsis

We consider the optimization problem min[F( g): g # X(0)], where F( g) is a variational energy associated to the obstacle g and the class X(0) of admissible obstacles is given by X(0)=[g: 0 Γ„ R : g on 0, 0 g dx=c] with # W 1, p 0 (0) and c # R fixed. Generally, this problem does not have a solution and it may happen that the ``optimal'' obstacle is of relaxed form. Under a monotonicity assumption on F, we prove the existence of a non-relaxed optimal obstacle in the family X(0) through a new method based on the notions of # and w#-convergences.

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