A characterization of solutions to a radially perturbed Laplace equation in the unit \(n\)-ball (Q1916854)

Denote by \(B^n\) the unit ball in \(\mathbb{R}^n\) and \((r, \vartheta)\) are polar coordinates on \(\mathbb{R}^n\). The objective of the paper is to characterize all solutions of the equation \[ \text{div}(\sigma/r)\text{ grad } u= 0\quad \text{in}\quad B^n, \] where \(\sigma\) has to satisfy some smoothness and growth conditions, but it is not assumed to be real analytic. The method used by the authors is separation of variables and the theory of ordinary differential equations, especially they use series expansions in spherical harmonics. Also the boundary behaviour of solutions is discussed.