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L2-regularity of minimizers of anisotropic interaction functionals
Abstract
We consider interaction functionals of the form ν↦ ℰ(ν)=∫_ℝN∫_ℝN W(x−y)intdν(y)intdν(x)+∫_ℝN V(x)intdν(x), involving an anisotropic kernel W and a general confinement potential V. Under standard assumptions on W and its Fourier transform, we show that the minimizer of ℰ has L2 density. Our argument relies on a careful analysis of nonlocal variational inequalities, which may be of independent interest.
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BibTeX
@misc{bulliongauthier2026l2regularity,
title = {{$L^2$-regularity of minimizers of anisotropic interaction functionals}},
author = {Tristan Bullion-Gauthier and Kai Xiao},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19181},
eprint = {2609.19181},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05743076v1},
}
RIS
TY - UNPB
TI - L^2-regularity of minimizers of anisotropic interaction functionals
AU - Tristan Bullion-Gauthier
AU - Kai Xiao
PY - 2026
DA - 2026/09/08
PB - HAL
DO - 10.48550/arxiv.2609.19181
UR - https://hal.science/hal-05743076v1
AB - We consider interaction functionals of the form ν↦ ℰ(ν)=∫_ℝ^N∫_ℝ^N W(x−y)intdν(y)intdν(x)+∫_ℝ^N V(x)intdν(x), involving an anisotropic kernel W and a general confinement potential V. Under standard assumptions on W and its Fourier transform, we show that the minimizer of ℰ has L^2 density. Our argument relies on a careful analysis of nonlocal variational inequalities, which may be of independent interest.
ER -