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arXiv · 2609.08297

Interior $W^{2,p}$ regularity for the sigma-$2$ equation

Yasheng Lyu
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Abstract

We prove that continuous $2$-convex solutions of the $\sigma_{2}$ equation with a density bounded above and below by positive constants belong to $W^{2,1}_{\mathrm{loc}}$ in every dimension. If, in addition, the density is continuous, the solutions belong to $W^{2,p}_{\mathrm{loc}}$ for every $1<p<\infty$.

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Yasheng Lyu. 2026-09-08. Interior $W^{2,p}$ regularity for the sigma-$2$ equation. https://arxiv.org/abs/2609.08297

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