| Title: |
Set-decomposition of normal rectifiable G-chains via an abstract decomposition principle |
| Authors: |
Goldman, Michael; Merlet, Benoît |
| Contributors: |
Centre de Mathématiques Appliquées de l'Ecole polytechnique (CMAP); Institut National de Recherche en Informatique et en Automatique (Inria)-École polytechnique (X); Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS); Reliable numerical approximations of dissipative systems (RAPSODI); Laboratoire Paul Painlevé - UMR 8524 (LPP); Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centre Inria de l'Université de Lille; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria); Université de Lille-Centre National de la Recherche Scientifique (CNRS); Department of Electronic & Electrical Engineering; INRIA RAPSODI; ANR-18-CE40-0013,SHAPO,Optimisation de forme(2018); ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011) |
| Source: |
ISSN: 0213-2230. |
| Publisher Information: |
CCSD; European Mathematical Society |
| Publication Year: |
2024 |
| Collection: |
LillOA (HAL Lille Open Archive, Université de Lille) |
| Subject Terms: |
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] |
| Description: |
International audience ; We introduce the notion of set-decomposition of a normal G-flat chain. We show that any normal rectifiable $G$-flat chain admits a decomposition in set-indecomposable sub-chains. This generalizes the decomposition of sets of finite perimeter in their ``measure theoretic" connected components due to Ambrosio, Caselles, Masnou and Morel. It can also be seen as a variant of the decomposition of integral currents in indecomposable components by Federer.As opposed to previous results, we do not assume that G is boundedly compact. Therefore we cannot rely on the compactness of sequences of chains with uniformly bounded N-norms. We deduce instead the result from a new abstract decomposition principle. As in earlier proofs a central ingredient is the validity of an isoperimetric inequality. We obtain it here using the finiteness of some h-mass to replace integrality. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/arxiv/2212.04752; ARXIV: 2212.04752 |
| DOI: |
10.4171/RMI/1504 |
| Availability: |
https://hal.science/hal-03890958; https://hal.science/hal-03890958v3/document; https://hal.science/hal-03890958v3/file/SetDecompositionOfGChains_revised.pdf; https://doi.org/10.4171/RMI/1504 |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.DA1D23CC |
| Database: |
BASE |