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On the absence of Eshelby property for non-ellipsoidal inclusions

✍ Scribed by V.A. Lubarda; X. Markenscoff

Book ID
104141515
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
361 KB
Volume
35
Category
Article
ISSN
0020-7683

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✦ Synopsis

It is shown that the Eshelby property does not hold for any inclusion bounded by a polynomial surface of higher than the second-degree, or any inclusion bounded by a non-convex surface. Inclusions bounded by segments of two or more different surfaces are also precluded. The absence of the Eshelby property for non-ellipsoidal inclusions is then discussed.

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Let N/M be an inclusion of von Neumann algebras with a conditional expectation E: M Γ„ N satisfying the finite index condition of [PiPo], i.e., there exists c>0 such that E(x) cx, \x # M + . In [Po4] we proved that such inclusions N/M satisfy the relative version of Dixmier's property, namely for any