A Strict Inclusion Related to Biharmonic Green's Functions of Clamped and Simply Supported Bodies.

摘要

Let O(N) sub beta and O(N) sub gamma be the classes of Riemannian N-manifolds, N > or = 2, which do not carry biharmonic Green's functions beta of clamped bodies, characterized by boundary data beta = d(beta)/dn = 0, or biharmonic Green's functions gamma of simply supported bodies, characterized by boundary data gamma = delta gamma = O, respectively. It is known that O(N) sub beta is a subset of O(N) sub gamma, but whether or not this inclusion is strict has been an open problem. This study shows that the inclusion is strict. (Author)