Analysis and Regularization of the Thin-Wire Integral Equation With Reduced Kernel

For the straight wire, modeled as a hollow tube, we establish a conditional equivalence relation between the integral equations with exact and reduced kernel. This relation allows us to examine the existence and uniqueness conditions for the integral equation with reduced kernel, based on a local argument. Further, we characterize the ill-posedness of integral equation with reduced kernel and we propose a regularization and filtering procedure to extend the range of this integral equation