PreprintarXiv licencearXiv
Interior W2,p regularity for the sigma-$2$ equation
Abstract
We prove that continuous $2$-convex solutions of the σ2 equation with a density bounded above and below by positive constants belong to W2,1loc in every dimension. If, in addition, the density is continuous, the solutions belong to W2,ploc for every 1<p<∞.
Related
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BibTeX
@misc{lyu2026interior,
title = {{Interior $W^2,p$ regularity for the sigma-$2$ equation}},
author = {Yasheng Lyu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08297},
eprint = {2609.08297},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08297},
}
RIS
TY - UNPB
TI - Interior W^2,p regularity for the sigma-$2$ equation
AU - Yasheng Lyu
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08297
UR - https://arxiv.org/abs/2609.08297
AB - We prove that continuous $2$-convex solutions of the σ_2 equation with a density bounded above and below by positive constants belong to W^2,1_loc in every dimension. If, in addition, the density is continuous, the solutions belong to W^2,p_loc for every 1<p<∞.
ER -