Construction of boundary operators for the laplacian. 11. Using of double layer potential

Abstract

I. Functional space Kr Let G be a bounded open C1 -set [I] in 23 the boundary of which is -smooth surface We write G= R3 U and introduce [2] on G, GC Sobolev spaces w2(c and ,, W (G') u e DLY(G'): u r, DUe c LjG),wee i o1)oeV paeS p2 (G) 2(lo } G1' t)I,t DXEt G) h re ts the distance of the point X E G' to the coordinate origin 0 and the space W2 (f) Introduce the space H' = 4(G) xW'(G') the elements of whlich we write as