Green Integrals on Manifolds with Cracks |
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Authors: | Schulze B-W Shlapunov A Tarkhanov N |
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Institution: | (1) Institut für Mathematik, Universität Potsdam, Postfach 60 15 53, 14415 Potsdam, Germany;(2) Krasnoyarsk State University, pr. Svobodnyi, 79, 660041 Krasnoyarsk, Russia;(3) Russian Academy of Sciences, Akademgorodok, Institute of Physics, 660036 Krasnoyarsk, Russia |
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Abstract: | We prove the existence of a limit in H
m
(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 Cauchyproblem 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 iterationsof the double layer potential. A similar regularisation is constructed also for a mixed problem in D. |
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Keywords: | Hodge theory Green formula boundary value problems |
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