TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Green integrals on manifolds with cracks N2 - We prove the existence of a limit in Hm(D) of iterations of a double layer potential constructed from the Hodge parametrix on a smooth compact manifold with boundary, X, and a crack S ⊂ ∂D, D being a domain in X. Using this result we obtain formulas for Sobolev solutions to the Cauchy problem in D with data on S, for an elliptic operator A of order m ≥ 1, whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of the double layer potential. A similar regularisation is constructed also for a mixed problem in D. T3 - Preprint - (2000) 12 Y1 - 2008 UR - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/2368 UR - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-25777 ER -