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Hessian estimates for special Lagrangian equation by doubling

Ravi Shankar
Vol. 19 (2026), No. 2, 339–352
DOI: 10.2140/apde.2026.19.339
Abstract

New doubling proofs are given for the interior Hessian estimates of the special Lagrangian equation. These estimates were originally shown by Chen, Warren and Yuan in CPAM 2009 and Wang and Yuan in AJM 2014. This yields a higher codimension analogue of Korevaar’s 1987 pointwise proof of the gradient estimate for minimal hypersurfaces, without using the Michael–Simon mean value inequality.

Keywords
special Lagrangian equation, interior estimates, partial regularity, Hessian equation
Mathematical Subject Classification
Primary: 35J93, 35J99
Milestones
Received: 16 March 2024
Revised: 26 August 2024
Accepted: 8 January 2025
Published: 22 January 2026
Authors
Ravi Shankar
Department of Mathematics
Princeton University
Princeton, NJ
United States
© 2026 MSP (Mathematical Sciences Publishers).

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