###
Invertibility of the biharmonic single layer potential operator

*Martin Costabel and Monique Dauge*
*Integral Equations and Operator Theory* **24** (1996) 46-67

PDF (204 k)

ps.gz (80 k)
codabih.ps.gz

The 2X2 system of integral equations corresponding to the biharmonic
single layer potential in the plane is known to be strongly
elliptic. It is also known to be positive definite on a space of
functions orthogonal to polynomials of degree one. We study the
question of its unique solvability without this orthogonality
condition. To each curve $\Gamma$, we associate a 4X4 matrix
$B_\Gamma$ such that this problem for the family of all curves
obtained from $\Gamma$ by scale transformations is equivalent to the
eigenvalue problem for $B_\Gamma$. We present numerical approximations
for this eigenvalue problem for several classes of curves.