Weak notions of Jacobian determinant and relaxation

Guido De Philippis

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 1, page 181-207
  • ISSN: 1292-8119

Abstract

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In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the distributional Jacobian and the relaxed total variation, which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex functionals.

How to cite

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De Philippis, Guido. "Weak notions of Jacobian determinant and relaxation." ESAIM: Control, Optimisation and Calculus of Variations 18.1 (2012): 181-207. <http://eudml.org/doc/221907>.

@article{DePhilippis2012,
abstract = {In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the distributional Jacobian and the relaxed total variation, which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex functionals. },
author = {De Philippis, Guido},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Distributional determinant; topological degree; relaxation; distributional determinant},
language = {eng},
month = {2},
number = {1},
pages = {181-207},
publisher = {EDP Sciences},
title = {Weak notions of Jacobian determinant and relaxation},
url = {http://eudml.org/doc/221907},
volume = {18},
year = {2012},
}

TY - JOUR
AU - De Philippis, Guido
TI - Weak notions of Jacobian determinant and relaxation
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2012/2//
PB - EDP Sciences
VL - 18
IS - 1
SP - 181
EP - 207
AB - In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the distributional Jacobian and the relaxed total variation, which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex functionals.
LA - eng
KW - Distributional determinant; topological degree; relaxation; distributional determinant
UR - http://eudml.org/doc/221907
ER -

References

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