On a conjecture for an overdetermined problem for the biharmonic operator

It has been proven that if the solution exists to an inhomogeneous biharmonic equation in the plane where the values of the solution, the normal derivative of the solution, and the Laplacian of the solution are prescribed on the boundary, then the domain is a disk. This result has been extended to NN-dimensions by the Serrin reflection method. Here we present a new proof and give a characterization of open balls in RnRn.