ON OVERDETERMINED BOUNDARY-VALUE-PROBLEMS FOR THE BIHARMONIC OPERATOR

We consider several overdetermined boundary value problems for the bih armonic operator and deduce that if a solution exists, then the domain must be a ball in N-space. When the auxiliary conditions are prescrib ed on the boundary, we reduce the problem to an equivalent second orde r overdetermined problem and use Rellich and Green identities and/or m aximum principle arguments. When one or more auxiliary condition is sp ecified on an interior surface, we use a particular solution of an ass ociated problem to obtain the result. (C) 1994 Academic Press, Inc.