Let X,Y ⊂ Rn be bounded domains of the same topological type. We are concerned with mappings f : X → Y, predominately orientation preserving homeomorphisms, in the Sobolev space W 1,p(X,Rn). Thus at almost every x 2 X the linear differential map Df (x) : TxX ≃ Rn -→ TyY ≃ Rn , y = f (x), is represented by the Jacobian matrix Df (x) 2 Rn×n + . Hereafter Rn×n + denotes the space of n × n-matrices with positive determinant.
|Original language||English (US)|
|Number of pages||106|
|Journal||Annali della Scuola normale superiore di Pisa - Classe di scienze|
|State||Published - 2020|
ASJC Scopus subject areas
- Theoretical Computer Science
- Mathematics (miscellaneous)