Hessian estimate for semiconvex solutions to the sigma-2 equation

Ravi Shankar, Yu Yuan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We derive a priori interior Hessian estimates for semiconvex solutions to the sigma-2 equation. An elusive Jacobi inequality, a transformation rule under the Legendre–Lewy transform, and a mean value inequality for the still nonuniformly elliptic equation without area structure are the key to our arguments. Previously, this result was known for almost convex solutions.

Original languageEnglish (US)
Article number30
JournalCalculus of Variations and Partial Differential Equations
Volume59
Issue number1
DOIs
StatePublished - Feb 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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