ASYMPTOTIC-BEHAVIOR OF THE SOLUTION OF THE INTEGRAL TRANSPORT-EQUATION IN THE VICINITY OF A CURVED MATERIAL INTERFACE

The differentiability properties of the solution phi of a linear integral equation arising in transport theory are considered. Two one-dimensional cases are considered, corresponding to either a spherically or a cylindrically symmetric domain in R**3. For such domains, a singular representation is derived showing explicitly the behavior of phi and its derivatives near the boundary of the domain. The representation is derived from certain basic properties of the integral transport operator T in Sobolev spaces.