Abstract

This paper studies the third problem for the Laplace equation on a bounded planar domain with inside cracks. The third condition u/n+hu=f is given on the boundary of the domain. The skip of the function u+u=g and the modified skip of the normal derivatives (u/n)+(u/n)+hu+=f are given on cracks. The solution is looked for in the form of the sum of a modified single-layer potential and a double-layer potential. The solution of the corresponding integral equation is constructed.