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Gradient Estimates for Hessian Equations with Measure Data
Abstract
In this article, we establish the interior gradient estimates for k-Hessian equations with measure data. We use the ideas from the potential theories for the p-Laplacian type equations and pointwise estimates of k-subharmonic functions by Labutin. The interior gradient regularity is optimal for kgeqslant3, while for k=2, we prove the interior W2,1+ε and C1,α estimates for $2$-subharmonic solutions.
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BibTeX
@misc{he2026gradient,
title = {{Gradient Estimates for Hessian Equations with Measure Data}},
author = {Rongxun He},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38846},
eprint = {2610.38846},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38846},
}
RIS
TY - UNPB
TI - Gradient Estimates for Hessian Equations with Measure Data
AU - Rongxun He
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38846
UR - https://arxiv.org/abs/2610.38846
AB - In this article, we establish the interior gradient estimates for k-Hessian equations with measure data. We use the ideas from the potential theories for the p-Laplacian type equations and pointwise estimates of k-subharmonic functions by Labutin. The interior gradient regularity is optimal for kgeqslant3, while for k=2, we prove the interior W^2,1+ε and C^1,α estimates for $2$-subharmonic solutions.
ER -