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.
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