PreprintCC BY 4.0arXiv
Functions of bounded variation are not dense in the Strong BD Norm
Abstract
We prove that functions of bounded variation are not dense in the space of functions of bounded deformation with respect to the strong BD norm. Using alternating Riesz products and directional slicing, we construct on every nonempty open subset of Rn (n≥2) a continuous, compactly supported BD function that is at positive distance from BV.
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BibTeX
@misc{lahti2026functions,
title = {{Functions of bounded variation are not dense in the Strong BD Norm}},
author = {Panu Lahti and Quoc-Hung Nguyen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21343},
eprint = {2610.21343},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21343},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Functions of bounded variation are not dense in the Strong BD Norm
AU - Panu Lahti
AU - Quoc-Hung Nguyen
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21343
UR - https://arxiv.org/abs/2610.21343
AB - We prove that functions of bounded variation are not dense in the space of functions of bounded deformation with respect to the strong BD norm. Using alternating Riesz products and directional slicing, we construct on every nonempty open subset of R^n (n≥2) a continuous, compactly supported BD function that is at positive distance from BV.
ER -