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Scattering of Acoustic and Electromagnetic Waves by Small Impedance Bodies of Arbitrary Shapes by Alexander G. Ramm

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CHAPTER 11

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SOME RESULTS FROM THE POTENTIAL THEORY

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11.1 Potentials of the simple and double layers.

Let D ⊂ image be a bounded domain with a boundary S C1,γ. This means that in local coordinates the equation of the surface is z = f (x, y), where z-axis is directed along the normal to S which points out of D and x, y are axes in the tangent plane to S at the origin, which is located on S. The function f (x, y) is continuously differentiable and

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