Green integrals on manifolds with cracks

Описание

Тип публикации: статья из журнала

Год издания: 2003

Идентификатор DOI: 10.1023/A:1024458312097

Ключевые слова: Hodge theory; Green formula; boundary value problems

Аннотация: 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 subset of partial derivative D, D being a domain in X. Using this result we obtain formulas for Sobolev solutions to the Cauchy problem in D with dПоказать полностьюata on S, for an elliptic operator A of order m greater than or equal to 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.

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Издание

Журнал: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY

Выпуск журнала: Vol. 24, Is. 2

Номера страниц: 131-160

ISSN журнала: 0232704X

Место издания: DORDRECHT

Издатель: KLUWER ACADEMIC PUBL

Авторы

  • Schulze B.-W. (Institut fur Mathematik,Universitat Potsdam)
  • Shlapunov A. (Krasnoyarsk State University)
  • Tarkhanov N. (Institute of Physics,Russian Academy of Sciences)

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