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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
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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.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1976
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