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Cauchy fluxes and Gauss–Green formulas for divergence-measure fields over general open sets

Abstract:

We establish the interior and exterior Gauss–Green formulas for divergence-measure fields in Lp over general open sets, motivated by the rigorous mathematical formulation of the physical principle of balance law via the Cauchy flux in the axiomatic foundation, for continuum mechanics allowing discontinuities and singularities. The method, based on a distance function, allows us to give a representation of the interior (resp. exterior) normal trace of the field on the boundary of any given ope...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00205-018-01355-4

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Keble College
Role:
Author, Author
ORCID:
0000-0001-5146-3839
Publisher:
Springer Publisher's website
Journal:
Archive for Rational Mechanics and Analysis Journal website
Volume:
233
Issue:
1
Pages:
87–166
Publication date:
2019-01-22
Acceptance date:
2018-12-19
DOI:
EISSN:
1432-0673
ISSN:
0003-9527
Pubs id:
pubs:953075
UUID:
uuid:66e3d11c-93df-4c5d-879a-b6618808ca79
Source identifiers:
953075
Local pid:
pubs:953075

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