## Strict $2$-convexity of convex solutions to the quadratic Hessian equation

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- by Connor Mooney PDF
- Proc. Amer. Math. Soc.
**149**(2021), 2473-2477 Request permission

## Abstract:

We prove that convex viscosity solutions to the quadratic Hessian inequality \begin{equation*} \sigma _2(D^2u) \geq 1 \end{equation*} are strictly $2$-convex. As a consequence we obtain short proofs of smoothness and interior $C^2$ estimates for convex viscosity solutions to $\sigma _2(D^2u) = 1$, which were proven using different methods in recent works of Guan-Qiu, McGonagle-Song-Yuan, and Shankar-Yuan.## References

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## Additional Information

**Connor Mooney**- Affiliation: Department of Mathematics, University of California Irvine, Irvine, California 92697
- MR Author ID: 1092639
- Email: mooneycr@math.uci.edu
- Received by editor(s): June 13, 2020
- Published electronically: March 25, 2021
- Additional Notes: This research was supported by NSF grant DMS-1854788.
- Communicated by: Ryan Hynd
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**149**(2021), 2473-2477 - MSC (2020): Primary 35J60, 35B65
- DOI: https://doi.org/10.1090/proc/15454
- MathSciNet review: 4246798