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The Quarterly Journal of Mechanics and Applied Mathematics 1976 29(4):487-492; doi:10.1093/qjmam/29.4.487
© 1976 by Oxford University Press
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EXTENSIONS OF A THEOREM OF HADAMARD ON AN INTEGRAL INEQUALITY IN THE CONTINUUM THEORY OF BIFURCATION

N. J. B. YOUNG

( Department of Applied Mathematics and Theoretical Physics, University of Cambridge Cambridge )

A well-known theorem of Hadamard states that in order for a certain integral inequality to hold in particular configurations of finite elastic bodies it is necessary that a condition, known as Hadamard's condition or Semi-Strong Ellipticity, holds at each point of the body. Several proofs of this result are known for compressible materials. This paper presents a proof of the theorem in a form suitable for bodies of, or partly of, incompressible material, using a modification of a proof by Noll (1). It is further shown that the conditions for the theorem may be considerably weakened.


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