Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

A change of variables formula for mappings in $\mathbf {BV}$

Author(s): Rustum Choksi; Irene Fonseca
Journal: Proc. Amer. Math. Soc. 125 (1997), 2065-2072.
MSC (1991): Primary 26B10, 26B30, 49Q20
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: A change of variables formula for mappings in $BV$ is obtained, where the usual jacobian is replaced by the determinant of the approximate differential.

References:

1.
Alberti, G. A Lusin type theorem for gradients. J. Funct. Anal. 100 (1991), 110-118. MR 92g:26018
2.
Ambrosio, L. On the lower semicontinuity of quasiconvex integrals in $SBV(\Omega , \mathbb {R}^k )$. Nonlinear Analysis Vol. 23, No. 3 (1994), 405-425. MR 95f:49011
3.
Ambrosio, L. and G. Dal Maso. A general chain rule for distributional derivatives. Proc. Amer. Math. Soc. 108 (1990), 691-702. MR 90j:26019
4.
Buttazzo, G. Energies on $BV$ and variational models in fracture mechanics. Preprint Dip. Mat. Univ. Pisa (1994).
5.
Choksi, R. and I. Fonseca. Bulk and Interfacial Energy Densities for Structured Deformations of Continua. To appear in Arch. Rat. Mech. Anal.
6.
De Giorgi, E and L. Ambrosio. Un nuovo tipo di funzionale del calculo delle vari azioni. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 82 (1988), 199-210. MR 92j:49043
7.
Evans, L. C. and R. F. Gariepy. Measure Theory and Fine Properties of Functions, CRC Press, 1992. MR 93f:28001
8.
Fonseca, I. and G. Francfort. Relaxation in $BV$ versus quasiconvexification in $W^{1,p}$; a model for the interaction between fracture and damage. Calc. Var. 4 (1995), 407-446. CMP 96:11
9.
Fonseca, I. and W. Gangbo. Degree Theory in Analysis and Applications. Oxford Univ. Press, 1995. MR 96k:47100
10.
Giaquinta, M., G. Modica and J. Sou[??]cek. Area and the Area Formula. Rend. Sem. Mat. Fis. Milano LXII (1992), 53-87. MR 95g:49079
11.
Morgan, F. Geometric Measure Theory: A Beginners Guide. Academic Press, Boston, 1988. MR 89f:49036
12.
Stein, E. Singular Integrals and Differentiability Properties of Functions. Princeton Univ. Press, Princeton, New Jersey, 1970.
13.
Ziemer, W. P. Weakly Differentiable Functions. Springer-Verlag, Berlin, 1989. MR 91e:46046

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 26B10, 26B30, 49Q20

Retrieve articles in all Journals with MSC (1991): 26B10, 26B30, 49Q20

Additional Information:

Rustum Choksi
Affiliation: Courant Institute, New York University, New York, New York 10012
Email: choksi@cims.nyu.edu

Irene Fonseca
Affiliation: Department of Mathematics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213
Email: fonseca@andrew.cmu.edu

DOI: 10.1090/S0002-9939-97-03793-3
PII: S 0002-9939(97)03793-3
Keywords: Functions of bounded variation, maximal function, approximate differential
Received by editor(s): December 1, 1995
Received by editor(s) in revised form: January 30, 1996
Communicated by: Jeffrey B. Rauch
Copyright of article: Copyright 1997, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google