My problem is the following: I have a bounded domain \Om in a plane, and I am looking for the fundamental solution
div_y C \nabla N (x,y) = \delta_x, in \Om
where C is the elasticity tensor (anisotropic), with natural Neumann boundary conditions on \partial \Om (traction free).
I don't ask for explicit solutions! I would like to know that
\nabla N(x-y) \le C/|x-y|, where C is a constant depending on whatever!
This is relevant in the study of the stress near a dislocation. Indeed I know the solution in all the plane, and I know how the stress decays in the all plane. I need to estimate the stress if the domain is bounded (how it is!!!)
Please, let me know if you know this result (or if you see that it is false!!!),
Thanks!