Year: 2025
Type: article
Abstract: We derive a priori interior Hessian estimates and interior regularity for the $\sigma_2$ equation in dimension four. Our method provides both a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher $(n\ge 5)$ dimensions.
Source: Annals of Mathematics
Authors: Ravi Shankar, Yu Yuan
Institutions: Princeton University, University of Washington
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408419084