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A relation between biharmonic Green’s functions of simply supported and clamped bodies

Published online by Cambridge University Press:  22 January 2016

James Ralston  and
Leo Sario
James Ralston
Affiliation:
University of California, Los Angeles
Leo Sario
Affiliation:
University of California, Los Angeles
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The deflection, under a point load, of a thin elastic plate clamped at the edges is the biharmonic Green’s function β with the boundary data β = ∂β/∂n = 0. If the boundary of the region is reasonably smooth, the construction of β offers no difficulty. In contrast, nothing is known about the existence of β in the general case. The purpose of our study is to give a sufficient condition for the existence of β on a given Riemannian manifold of arbitrary dimension and to construct β. Our results will have, apart from their physical meaning in elasticity, consequences in the biharmonic classification theory of Riemannian manifolds.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 61 , July 1976 , pp. 59 - 71
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

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