On the potential of a solenoidal vector field
type: Item
instance of: scholarly article
title: On the potential of a solenoidal vector field
zbMATH Open document ID: 0727.35030
DOI: 10.1016/0022-247X(90)90166-D
author: Ton Tran-Cong
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: The author constructs one solution to rot u\(=f\) in an unbounded domain (star shaped with respect to a sphere) for a differentiable vector field f (not necessarily vanishing at infinity) provided the necessary conditions div f\(=0\), \(\int_{S}f\cdot \nu =0\) (if S is an interval boundary part) hold. Necessary and sufficient conditions for solving rot u\(=f\in L_ p\) with \(u|_{\partial G}=0\) for bounded and (if \(p<3)\) unbounded domains of a more difficult structure by means of potential theory can be found e.g. in \textit{W. von Wahl} [Lect. Notes Math. 1431, 152-157 (1990; Zbl 0719.35015)].
Mathematics Subject Classification ID: 35F05
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 4200715
zbMATH Keywords: curl
zbMATH Keywords: unbounded domain
reviewed by: Michael Wiegner
MaRDI profile type: Publication
cites work: Q5795766
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description: scientific article; zbMATH DE number 4200715