Nonuniqueness in the integral equation formulation of the biharmonic equation in multiply connected domains (Q1094206)

In the boundary integral equation method, the biharmonic equation is converted to a pair of integral equations by using Green's third identity. In multiply connected domains, for a particular exceptional geometry the integral equations do not have a unique solution. Additional constraint equations are derived to enforce uniqueness in such situations. Two example problems are solved to demonstrate the effectiveness of the constraints.