Тип публикации: статья из журнала
Год издания: 2001
Аннотация: We prove existence of the Hp(D)-limit for iterations of the double layer potentials constructed from a Hodge parametrix on a smooth compact manifold X (here D is an open connected subset in X). The limit is the orthogonal projection of the Sobolev space Hp(D) onto the closed subspace of Hp(D)-solutions of some elliptic operator P oПоказать полностьюf order p?1. Using this result, we obtain a formula for Sobolev solutions to the equation Pu=f in D if such exist. Solutions are given in the form of series whose summands are iterations of the double layer potentials. We also construct a similar expansion for the Neumann P-problem in D.
Журнал: Siberian Mathematical Journal
Выпуск журнала: Т. 42, № 4
Номера страниц: 801-810
ISSN журнала: 00374466
Место издания: Новосибирск
Издатель: Springer-Verlag GmbH