Abstract
We give global estimates on some potential of functions in a bounded domain of the Euclidean space R-n (n >= 2). These functions may be singular near the boundary and are globally comparable to a product of a power of the distance to the boundary by some particularly well behaved slowly varying function near zero. Next, we prove the existence and uniqueness of a positive solution for the integral equation u - V(au(sigma)) with 0 <= sigma < 1, where V belongs to a class of kernels that contains in particular the potential kernel of the classical Laplacian V = (-Delta)(-1) or the fractional laplacian V = (-Delta)(alpha/2), 0< alpha <2.