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The Characterisation of the Regularity of the Jacobian Determinant in the Framework of Potential Spaces
Author(s) -
Sickel Winfried,
Youssfi Abdellah
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798006735
Subject(s) - jacobian matrix and determinant , bounded function , mathematics , operator (biology) , pure mathematics , algebra over a field , discrete mathematics , mathematical analysis , chemistry , biochemistry , repressor , transcription factor , gene
We give necessary and sufficient conditions on the parameters s 1 , s 2 , …, s m , p 1 , p 2 , …, p m such that the Jacobian determinant extends to a bounded operator fromH p 1s 1× H p 2s 2× … × H p ms minto Z′. Here all spaces are defined on R n and 2⩽ m ⩽ n . In almost all cases the regularity of the Jacobian determinant is calculated exactly.