May be, you can find these books in internet.

Discontinuities in the Electromagnetic Field

M. Mithat Idemen

Analytical techniques in the theory of guided waves

Ráj Mittra, ‎S. W. Lee - 1971

Quick Finite Elements for Electromagnetic Waves

Giuseppe Pelosi, ‎Roberto Coccioli, ‎Stefano Selleri - 1998

The edges and corners create troubles  in the Greens function solutions  of Laplace and elastic  problems in Boundary Element methods when one applies Dirichlet and Neumann boundary conditions.  Which generate integral equations of the  first and second kinds, respectively. The proofs of existence for these two kinds of integral equations met in theory of elasticity are similar to those in Laplace based cases (EM, solutions of electrostatic field, solution of steady state heat flow in interconnect lines, etc. ) there are however important differences in the surface and functional smoothness requirements, and  in the interpretation of the integral appeared on Neumann BC that results the Fredholm integral equation of the second kind applies, and it can be shown that the solutions exist.  Boundary S  must now be a Lyapunov surface and traction vector should be Hölder continuous, and the Cauchy principal value of the integral   must be taken....

All my work last 15 years went by  handling very sophisticated practical problems ( surface instabilities, electromigration, grain boundary grooving, quantum dots etc.)  using our home-made coded  indirect boundary element method, which uses simplest and more accurate straight linear elements in 2D (the flat triangular elements  in 3D) problems that can easily by pass the corners and edges. For the time integration of course one has to utilize the simplest technique, which is Euler integration scheme (exception:Thermal stress problem) since one has constantly varying  linear element lengths from one time step to another. For the time varying thermal stress gradient evaluations, we had to  use body forces as well without too much difficulties. 

Best Regars

Edge singularity is rather old problem. To find the type of the singularity you should deal with the Green formula. You can consult with books in Diffraction theory (acoustic, electromagnetic) in which the problem is described in details. Shortly, the edge leads to the singularity but you need uniqueness of the solution. From this condition one obtains the appropriate singularity type. For the Laplace or Helmholtz operator it is so-called Meixner's Edge Condition (convergence of integral of the square of gradient over domain containing the edge). You can follow the scheme of obtaining the Meixner's Edge Condition for your operator and come to proper condition. If you have only planes intersection the condition will be, really, the same as for 2D case (with natural correction taking into account the third coordinate). Conical point gives another result. 

Dr. Popov,  I thank you for your advice! What we call in English as well as in German languages is that:   ^One  heats up the old soup^. Unfortunately,  I don't  have to consult any books  since there is no book left  on the market  to be consulted any more, I was talking about the Boundary Element method as you might know one doesn't have any other chance but to use the Greens Functions. I am not a professional  mathematicians Thanks God!. All I have to do when it comes to a point where the curvature becomes so-called infinite I just filled it to smoothen out that region. That is what we do in the numerical implementation of the problem. And leave the rest to the mathematicians to prove that there exist a solution indeed!  ^Smirnoff, V. I (1964) A course of Higher Mathematics^.

In Boundary Element (BE) method, The derivation of the integral equation for the Neumann Boundary condition,  is valid if only if  the argument  of the free term, which is also called the density function  denoted by mu( Q) ,   does not lie on an edge or corner (EC) of the boundary. This difficult is over come as I mentioned above by using simple numerical implementation as such that  Q  point is placed at the centroid of each of the BE in turn and so BC is satisfied exactly at each centroid, subjected to the assumption that the density function mu(Q) is constant over the each element. The requirement  that   Q  lies on a smooth part of the boundary is automatically satisfied in the nodal collocation scheme.  One has great trouble however, if one proposed density functions, which  are varying   linearly  or in higher orders along the boundary elements!!!

For the traction boundary conditions of elasticity , the Cauchy principal value of the integral appearing in the boundary integral equation must be evaluated . This is a simple matter in the numerical implementation out line above, However if curved elements or elements with higher order variations of the density function  are to be used and so it becomes necessary to resort the numerical integration, care must be taken to ensure that numerical integration schemes do correctly evaluate Cauchy principal values.

I have found that to use the simplest scheme is the most reliable and fast approach to the problem, while doing that we have checked  our results applying the scheme to those quasi-polygons where one has exact analytically solutions!

Best Regards

May be, you can find these books in internet.

Discontinuities in the Electromagnetic Field

M. Mithat Idemen

Analytical techniques in the theory of guided waves

Ráj Mittra, ‎S. W. Lee - 1971

Quick Finite Elements for Electromagnetic Waves

Giuseppe Pelosi, ‎Roberto Coccioli, ‎Stefano Selleri - 1998

Dear Dr. Popov, I thank you for your list.  I was just joking when I said 'no books left to be read!  I have a set of articles (Craster & Shain etc.) on the Laplace Operator, which are interesting in on the diffraction and scattering of  EW.  But how about the elasticity?  All they admit that up to now no acceptable or manageable solution of singularity appeared any where in the literature.  Best Regards

Note: I have solved very important singularity problem nothing to with the Laplace or Helmholtz  but related to  dynamics of the grain boundary triple junctions motion formulated by the  irreversible thermodynamics. 

I will check all those articles you have kindly commented above. Thanks again.