Hessian estimate for semiconvex solutions to the sigma-2 equation

Ravi Shankar; Yu Yuan

doi:10.1007/s00526-019-1690-1

Hessian estimate for semiconvex solutions to the sigma-2 equation

Ravi Shankar
, Yu Yuan

Research output: Contribution to journal › Article › peer-review

14 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 language	English (US)
Article number	30
Journal	Calculus of Variations and Partial Differential Equations
Volume	59
Issue number	1
DOIs	https://doi.org/10.1007/s00526-019-1690-1
State	Published - Feb 1 2020
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1007/s00526-019-1690-1

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title = "Hessian estimate for semiconvex solutions to the sigma-2 equation",

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.",

author = "Ravi Shankar and Yu Yuan",

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AB - 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.

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UR - https://www.scopus.com/pages/publications/85077714886#tab=citedBy

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M3 - Article

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JO - Calculus of Variations and Partial Differential Equations

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IS - 1

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Hessian estimate for semiconvex solutions to the sigma-2 equation

Abstract

All Science Journal Classification (ASJC) codes

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