# Weak notions of Jacobian determinant and relaxation

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

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

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topDe 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 -

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