What do the eigenfunctions look like? I didn't know the circular disk was such an exotic problem for Laplace's equation. edit: Ah, I misunderstood the problem.

What do the eigenfunctions look like? I didn't know the circular disk was such an exotic problem for Laplace's equation. edit: Ah, I misunderstood the problem. The eigenfunctions are exactly solved; the problem of sorting and ordering their eigenvalues is apparently not! From their page 4, - "Although all the eigenvalues of the Dirichlet and Neumann Laplacians on the unit disk are explicitly known in terms of zeros of the Bessel functions or their derivatives, see §2 below, in each case the spectrum is given by a two-parametric family, and rearranging it into a single monotone sequence appears to be an unfeasible task." https://arxiv.org/abs/2203.07696 https://arxiv.org/abs/2203.07696