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Regularization for some boundary integral equations of the first kind in mechanics. (English) Zbl 0946.35108
The authors show how to regularize some boundary integral equations. They are particularly dealing with the following problems: Laplace equation, the Stokes system and the Lamé equations. Studying the singular integral systems in which the unknown is a vector whose components are scalar functions while the data is a vector of differential forms they prove the following result: The solution of each considered problem can be given as a single layer potential with a specified density.

MSC:
35Q72Other PDE from mechanics (MSC2000)
31B10Integral representations of harmonic functions (higher-dimensional)
65R32Inverse problems (integral equations, numerical methods)