A Relation Between Biharmonic Green's Functions of Simply Supported and Clamped Bodies.

摘要

The deflection, under a point load, of a thin elastic plate clamped at the edges is the biharmonic Green's function beta with the boundary data beta= the derivative of partial beta/partial n=O. If the boundary of the region is reasonably smooth, the construction of beta offers no difficulty. In contrast, nothing is known about the existence of beta in the general case. The purpose of our study is to give a sufficient condition for the existence of beta on a given Riemannian manifold of arbitrary dimension and to construct beta. Our results will have, apart from their physical meaning in elasticity, consequences in the biharmonic classification theory of Riemannian manifolds.