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A general converse theorem for mean‐value theorems in linear elasticity
Author(s) -
Mitrea Dorina,
Rosenblatt Heather
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.725
Subject(s) - converse , mathematics , elasticity (physics) , mathematical analysis , mean value , geometry , statistics , materials science , composite material
We prove a rather general mean‐value formula in the theory of elasticity, which expresses the value of the displacement at the centre of a sphere in terms of certain combinations of integral averages over the sphere itself of the traction and the displacement. We also establish the corresponding converse to this mean‐value formula under minimal smoothness assumptions on the displacement. Copyright © 2006 John Wiley & Sons, Ltd.