I am working on some boundary integral equation formulation and I am currently stuck with some mathematics. I wish anyone can help me out with this.
I have an anisotropic (sometimes called generalized) biharmonic differential operator which takes the form
L = k11 D1^4 + k12 D1^2 D2^2 + k22 D2^4
where D1 = d/dx, D2 = d/dy, my problem is two dimensional.
I need to find a fundamental solution (Green's function) for this operator, that is
L(u) = -delta
where delta is Dirac delta function.