PreprintCC BY-NC-ND 4.0arXiv
Weakly Lipschitz mappings in higher dimensions
Abstract
We introduce and investigate the main features of weakly Lipschitz mappings whose pointwise Lipschitz constant is controlled from above by the derivative of a set function. The main results give conditions under which such mappings belong to W1,nloc, and show that the class contains metrically quasiconformal mappings as a proper subclass. In addition, under a Rado--Reichelderfer type oscillation assumption, we derive diameter control, image-measure bounds, sufficient conditions for Lusin's (N)-property, and an area formula.
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BibTeX
@misc{golberg2026weakly,
title = {{Weakly Lipschitz mappings in higher dimensions}},
author = {Anatoly Golberg},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03532},
eprint = {2611.03532},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03532},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Weakly Lipschitz mappings in higher dimensions
AU - Anatoly Golberg
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03532
UR - https://arxiv.org/abs/2611.03532
AB - We introduce and investigate the main features of weakly Lipschitz mappings whose pointwise Lipschitz constant is controlled from above by the derivative of a set function. The main results give conditions under which such mappings belong to W^1,n_loc, and show that the class contains metrically quasiconformal mappings as a proper subclass. In addition, under a Rado--Reichelderfer type oscillation assumption, we derive diameter control, image-measure bounds, sufficient conditions for Lusin's (N)-property, and an area formula.
ER -