Invertibility of the biharmonic single layer potential operator
نویسندگان
چکیده
Martin COSTABEL & Monique DAUGE Abstract. The 2 2 system of integral equations corresponding to the biharmonic single layer potential in R2 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 , we associate a 4 4 matrix B such that this problem for the family of all curves obtained from by scale transformations is equivalent to the eigenvalue problem for B . We present numerical approximations for this eigenvalue problem for several classes of curves.
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