Geodesic
Change of variables formula under minimal assumptions
Colloquium Mathematicum, Tome 64 (1993) no. 1, pp. 93-101

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

In the previous papers concerning the change of variables formula (in the form involving the Banach indicatrix) various assumptions were made about the corresponding transformation (see e.g. [BI], [GR], [F], [RR]). The full treatment of the case of continuous transformation is given in [RR]. In [BI] the transformation was assumed to be continuous, a.e. differentiable and with locally integrable Jacobian. In this paper we show that none of these assumptions is necessary (Theorem 2). We only need the a.e. existence of approximate partial derivatives. In Section 3 we consider the general form of the change of variables formula for Sobolev mappings. The author wishes to thank Professor Bogdan Bojarski for many stimulating conversations and suggestions. 
Piotr Hajłasz. Change of variables formula under minimal assumptions. Colloquium Mathematicum, Tome 64 (1993) no. 1, pp. 93-101. doi: 10.4064/cm-64-1-93-101
@article{10_4064_cm_64_1_93_101,
     author = {Piotr Haj{\l}asz},
     title = {Change of variables formula under minimal assumptions},
     journal = {Colloquium Mathematicum},
     pages = {93--101},
     year = {1993},
     volume = {64},
     number = {1},
     doi = {10.4064/cm-64-1-93-101},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-64-1-93-101/}
}
TY  - JOUR
AU  - Piotr Hajłasz
TI  - Change of variables formula under minimal assumptions
JO  - Colloquium Mathematicum
PY  - 1993
SP  - 93
EP  - 101
VL  - 64
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-64-1-93-101/
DO  - 10.4064/cm-64-1-93-101
LA  - en
ID  - 10_4064_cm_64_1_93_101
ER  - 
%0 Journal Article
%A Piotr Hajłasz
%T Change of variables formula under minimal assumptions
%J Colloquium Mathematicum
%D 1993
%P 93-101
%V 64
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-64-1-93-101/
%R 10.4064/cm-64-1-93-101
%G en
%F 10_4064_cm_64_1_93_101

Cité par Sources :