Malmheden's theorem revisited (Q607070)

Malmheden proved that the value of a harmonic function at any point in a disk or in a ball can be computed from its values on the boundary by an algorithm (the solution to the Dirichlet problem in a ball). In the present paper, the authors provide an alternative approach to Malmheden's theorem, which admits a generalization to polyharmonic functions. Furthermore, applications, which reveal geometric properties of the harmonic measure in \(n\)-dimensional balls, are given. The paper is well written, with many historical details concerning the evolution of the corresponding mathematical proofs.