Free Terms and Compatibility Conditions for 3D Hypersingular Boundary Integral Equations

In this paper two basic issues concerning hypersingular boundary integral equations (HBIE's) for three-dimensional problems are addressed. Firstly, a new general method for the evaluation of all free-term coefficients is presented. Secondly, the so-called Tricomi-Mikhlin compatibility conditions at non-smooth bounday points are proved. In both cases, the analysis is performed in the parametric space and with deep recourse to differential geometry. The final formulas are quite simple, Numerical results are provided to test these theoretical findings.

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