Hessian estimates for the sigma-2 equation in dimension four

2023/05/21 by Ravi Shankar, Yu Yuan, Shankar, Ravi +1 · 7 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2305.12587

openalex publication_date 2023/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a priori interior Hessian estimates and interior regularity for the σ₂ equation in dimension four. Our method provides respectively a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher n≥ 5 dimensions.

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