Shizan Fang, Integration by Parts Formula and Logarithmic Sobolev Inequality on the Path Space over Loop Groups, The Annals of Probability, Vol. 27, No. 2 (Apr., 1999), pp. 664-683 ...

We consider boundary integral equations of the first kind with logarithmic kernels on smooth closed or open contours in R2. Instead of solving the first kind equations directly, we propose a fully ...