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What is known about the quadruple layer potential in 3D (on closed smooth surfaces)? In terms of jump relations, continuity on Hölder Spaces (and/or Sobolev spaces), and Calderon-type identities (regularization). I'm interested in the Laplace and also the Helmholtz case (the acoustic problem). Thanks

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Is this the same as the hypersingular integral potential? –  timur Sep 11 '11 at 3:17
    
Timur, no- the kernel is of the form $\frac{\partial^2 G}{\partial n_x^2}(x,y)$. –  Nilima Nigam Sep 11 '11 at 3:27
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up vote 2 down vote accepted

Here's a reference to a paper by Shidong Jiang which may be useful as regards jump relations : http://web.njit.edu/~jiang/Papers/jump.pdf

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