A homotopy operator for Spencer's sequence in the C?-case

Описание

Тип публикации: статья из журнала

Год издания: 2009

Идентификатор DOI: 10.3103/S1055134409020035

Ключевые слова: Formal complexes, Homotopy operator, Overdetermined system, Poincare lemma, Spencer's sequence

Аннотация: The main result of the formal theory of overdetermined systems of differential equations says that any regular system Au = f with smooth coefficients on an open set U ? ?n admits a solution in smooth sections of the bundle of formal power series provided that f satisfies a compatibility condition in U. Our contribution consists in Показать полностьюdetailed study of the dependence of formal solutions on the point of the base U of the bundle. We also parameterize these solutions by their Cauchy data. In doing so, we prove that, under absence of topological obstructions, there is a formal solution which smoothly depends on the point of the base. This leads to a concept of a finitely generated system (do not mix up it with holonomic or finite-type systems) for which we then prove a C?-Poincare lemma. © Allerton Press, Inc. 2009.

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Издание

Журнал: Siberian Advances in Mathematics

Выпуск журнала: Vol. 19, Is. 2

Номера страниц: 91-127

ISSN журнала: 10551344

Авторы

  • Shlapunov A.A. (Institute of Mathematics,Siberian Federal University)
  • Tarkhanov N.N. (Institute of Mathematics,University of Potsdam)

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