### On boundary element methods for solving elliptic boundary value problems

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Simple examples of bounded domains $D\subset {\mathbf{R}}^{3}$ are considered for which the presence of peculiar corners and edges in the boundary $\delta D$ causes that the double layer potential operator acting on the space $\mathcal{S}\left(\delta D\right)$ of all continuous functions on $\delta D$ can for no value of the parameter $\alpha $ be approximated (in the sub-norm) by means of operators of the form $\alpha I+T$ (where $I$ is the identity operator and $T$ is a compact linear operator) with a deviation less then $\left|\alpha \right|$; on the other hand, such approximability turns out to be possible for...

We present a method for the construction of artificial far-field boundary conditions for two- and three-dimensional exterior compressible viscous flows in aerodynamics. Since at some distance to the surrounded body (e.g. aeroplane, wing section, etc.) the convective forces are strongly dominant over the viscous ones, the viscosity effects are neglected there and the flow is assumed to be inviscid. Accordingly, we consider two different model zones leading to a decomposition of the original flow...

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