PreprintCC0arXiv
The Liouville property for entire local minimizers from the space BVloc(R2,RN) of variational integrals with linear growth
Abstract
We consider functions u : R2 → RN from the class Bloc which locally minimize the relaxed version of a variational integral with a strictly convex density being in addition of linear growth. It turns out that the boundedness of entire local minimizers u implies their constancy.
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BibTeX
@misc{bildhauer2026liouville,
title = {{The Liouville property for entire local minimizers from the space $BV_\mathrmloc(\R^2,\R^N)$ of variational integrals with linear growth}},
author = {Michael Bildhauer and Martin Fuchs},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14321},
eprint = {2610.14321},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14321},
note = {CC0},
}
RIS
TY - UNPB
TI - The Liouville property for entire local minimizers from the space BV_loc(R^2,R^N) of variational integrals with linear growth
AU - Michael Bildhauer
AU - Martin Fuchs
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.14321
UR - https://arxiv.org/abs/2610.14321
AB - We consider functions u : R^2 → R^N from the class Bloc which locally minimize the relaxed version of a variational integral with a strictly convex density being in addition of linear growth. It turns out that the boundedness of entire local minimizers u implies their constancy.
ER -