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 Calderontype identities (regularization). I'm interested in the Laplace and also the Helmholtz case (the acoustic problem). Thanks

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 

