TY  - INPR
A1  - Shlapunov, Alexander
T1  - On Iterations of double layer potentials
N2  - We prove the existence of Hp(D)-limit of iterations of double layer potentials constructed with the use of Hodge parametrix on a smooth compact manifold X, D being an open connected subset of X. This limit gives us an orthogonal projection from Sobolev space Hp(D) to a closed subspace of Hp(D)-solutions of an elliptic operator P of order p ≥ 1. Using this result we obtain formulae for Sobolev solutions to the equation Pu = f in D whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of double layer potentials. Similar regularization is constructed also for a P-Neumann problem in D.
T3  - Preprint - (2000) 02 
Y1  - 2008
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/2359
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-25687
ER  -