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
Summary: This paper studies the third problem for the Laplace equation on a bounded planar domain with inside cracks. The third condition \(\partial u/\partial n+hu=f\) is given on the boundary of the domain. The skip of the function \(u_{+} - u_{ - }=g\) and the modified skip of the normal derivatives \((\partial u/\partial n)_+ - (\partial u/\partial n)_- +hu_{+}=f\) 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.
scientific article; zbMATH DE number 5164244