Hypersingularity at sharp edges: Is it physical and worth studying?

Hypersingularity is a theoretical electromagnetic phenomenon that may occur at the mathematically sharp edge of a wedge formed by an ordinary dielectric and a lossless metal having finite and negative permittivity. The singularity of the transverse electric field component at the edge is so strong that to date all well-established numerical methods for solving electromagnetic scattering problems have failed to converge whenever hypersingularity occurs. Unable to find quick solutions to the non-convergence problem, people begin to ask: Is hypersingularity physical? Some pointed out that Meixner´s edge condition is violated. I show that the edge condition is not applicable to the present case, and if it were it would not be violated. With a proper combination of the two degenerate hypersingular modes the energy-flux edge condition is satisfied. Therefore, it is insufficient to consider that hypersingularity is unphysical solely based on energy considerations. I also remark on the possible illposedness of the hypersingularity problem without imposition of the right edge condition.