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PreprintarXiv licencearXiv

A new approach to interior estimates for fully nonlinear elliptic equations

  • Jui-Yun Hung
  • Jiakun Liu
  • Neil Trudinger
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Abstract

We give new proofs of interior second derivative estimates for the Monge-Ampère equation and the constant quadratic Hessian equation, based on the two-point maximum principle. The arguments require only one differentiation of the equation. For the Monge-Ampère equation, the inhomogeneous term is assumed to be positive and continuously differentiable. For the quadratic Hessian equation, the estimate holds in every dimension n≥2.

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Cite

BibTeXRIS
BibTeX
@misc{hung2026approach,
  title = {{A new approach to interior estimates for fully nonlinear elliptic equations}},
  author = {Jui-Yun Hung and Jiakun Liu and Neil Trudinger},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15457},
  eprint = {2610.15457},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15457},
}
RIS
TY  - UNPB
TI  - A new approach to interior estimates for fully nonlinear elliptic equations
AU  - Jui-Yun Hung
AU  - Jiakun Liu
AU  - Neil Trudinger
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.15457
UR  - https://arxiv.org/abs/2610.15457
AB  - We give new proofs of interior second derivative estimates for the Monge-Ampère equation and the constant quadratic Hessian equation, based on the two-point maximum principle. The arguments require only one differentiation of the equation. For the Monge-Ampère equation, the inhomogeneous term is assumed to be positive and continuously differentiable. For the quadratic Hessian equation, the estimate holds in every dimension n≥2.
ER  -