PreprintCC BY 4.0arXiv
Gradient potential estimates for k-Hessian equations
Abstract
For 2≤ k<n, we prove pointwise gradient bounds for proper weak k-convex functions in terms of a local average and a Wolff potential of the full Hessian measure Fk[u]. The estimate yields local Lipschitz regularity for Fk[u]=f with f∈ Ln/k,1/kloc, and for Fk[u]=|Du|p when 0<p<nk/(n−k). Both the Lorentz index 1/k and the upper bound on p are sharp.
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BibTeX
@misc{liu2026gradient,
title = {{Gradient potential estimates for k-Hessian equations}},
author = {Huajie Liu and Shiguang Ma and Shengyang Zang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08184},
eprint = {2611.08184},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08184},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gradient potential estimates for k-Hessian equations
AU - Huajie Liu
AU - Shiguang Ma
AU - Shengyang Zang
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08184
UR - https://arxiv.org/abs/2611.08184
AB - For 2≤ k<n, we prove pointwise gradient bounds for proper weak k-convex functions in terms of a local average and a Wolff potential of the full Hessian measure F_k[u]. The estimate yields local Lipschitz regularity for F_k[u]=f with f∈ L^n/k,1/k_loc, and for F_k[u]=|Du|^p when 0<p<nk/(n−k). Both the Lorentz index 1/k and the upper bound on p are sharp.
ER -