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

international journal of mathematics and mathematical sciences

The solution of the third problem for the Laplace equation on planar domains with smooth boundary and inside cracks and modified jump conditions on cracks