Local Change of Coordinates for Grid-Functions on Regions with Curved Boundary

Local change of coordinates, providing an appropriate transformation of functions on a domain Ω ∩ Rn into functions on Rn and R+n, is a well‐known and frequently used technical tool in the theory of Sobolev‐spaces Wm,p (Ω) and partial differential equations. In this paper we propose a corresponding...

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Bibliographic Details
Published in:Mathematische Nachrichten 1988, Vol.139 (1), p.45-61
Main Author: Kornhuber, R.
Format: Article
Language:English
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Summary:Local change of coordinates, providing an appropriate transformation of functions on a domain Ω ∩ Rn into functions on Rn and R+n, is a well‐known and frequently used technical tool in the theory of Sobolev‐spaces Wm,p (Ω) and partial differential equations. In this paper we propose a corresponding transformation mapping grid‐functions on regular grids Ωh into functions on Rnh and Rnh,+ which as in the continuous case can be used to remedy various difficulties arising the curved boundary of Ω.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.19881390106