On the Cauchy problem for the Dolbeault complex in spaces of distributions

Описание

Тип публикации: статья из журнала

Год издания: 2013

Идентификатор DOI: 10.1080/17476933.2012.697459

Ключевые слова: Cauchy problem, Cauchy-Riemann operator, Dolbeault complex, Hilbert space methods

Аннотация: Let D be a bounded domain in C-n(n1) with C-smooth boundary D. We indicate appropriate Sobolev spaces of negative smoothness to study the non-homogeneous Cauchy problem for the Dolbeault complex. We give an adequate formulation of the problem and describe its necessary and sufficient solvability conditions. In the Lebesgue space L-Показать полностью2(D) we construct approximate and exact solutions to the Cauchy problem with maximal possible regularity. In particular, we construct Carleman's formulae for a differential form u with coefficients from the Sobolev space H-1(D), by the value of its complex tangential part (u) on an open (in the topology of D) connected set Gamma subset of partial derivative D and the value of its complex differential (partial derivative) over baru, in D modulo (partial derivative) over bar -exact form with the tangential part vanishing on Gamma (at least if partial derivative D\Gamma is strictly pseudo-convex). Also an instructive example is considered.

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Издание

Журнал: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS

Выпуск журнала: Vol. 58, Is. 11

Номера страниц: 1591-1614

ISSN журнала: 17476933

Место издания: ABINGDON

Издатель: TAYLOR & FRANCIS LTD

Авторы

  • Fedchenko D. (Institute of Core Undergraduate Programs,Siberian Federal University)
  • Shlapunov A. (Institute of Mathematics,Siberian Federal University)

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