On the Regularity of Solutions of Nonlinear Integral Equations

摘要

The smoothness of the solution to a class of nonlinear (Urysohn) integral equations is discussed. The kernel of the integral operator may have weak diagonal and boundary singularities, information about them is given by certain estimations. Showing that the solution belongs to a special weighted space of smooth functions, the growth of the derivatives of the solution near the boundary of the domain of integration is described.