An Elementary Proof That the Biharmonic Green Function of an Eccentric Ellipse Changes Sign

Abstract

P R. Garabedian showed in 1951 that the Green function for the biharmonic boundary value problem with vanishing Dirichlet data changes sign in case the domain is a sufficiently eccentric ellipse. This refuted a conjecture made by J. Hadamard in 1908. The proof of Garabedian was based on kernel functions; the present note gives an elementary proof.