A nuclear approach to solving the equation \(Pu=f\) for an elliptic complex P
type: Item
instance of: scholarly article
title: A nuclear approach to solving the equation \(Pu=f\) for an elliptic complex P
zbMATH Open document ID: 0592.58041
DOI: 10.1007/BF00968906
author: B. George
published in: Siberian Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: \textit{W. Koppelman}'s formula [Bull. Am. Math. Soc. 73, 554-556 (1967; Zbl 0186.138)] and \textit{F. Norguet}'s formula [Lect. Notes Math. 409, 1- 97 (1974; Zbl 0307.32004)] are generalized for an elliptic complex P. The tangent complex \(P_ B\) is associated to P and the problem of the exactness of the Mayer-Vietoris sequence of P and of the pair (\({\bar \Omega}\),c\(\Omega)\), \(\Omega\) being a domain with regular boundary, is analysed. The homotopy formulas are proved. Also, the compact support solution for the equation \(Pu=f\) is given. Finally the problem of the prolongation to the boundary for the complex P is formulated and analysed; the solution of the tangent equation on the boundary, \(P_ Bu^ 0=f^ 0\), is given. These results include as particular cases the corresponding results known for the Dolbeault complex \({\bar \partial}\) and de Rham complex \(\partial\).
Mathematics Subject Classification ID: 58J10
zbMATH DE Number: 3951651
zbMATH Keywords: fundamental solution
zbMATH Keywords: elliptic complex
zbMATH Keywords: Mayer-Vietoris sequence
zbMATH Keywords: Dolbeault complex
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3951651