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

7 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

Access to Document

10.1007/s00526-019-1690-1

Cite this

@article{a6a554e754f84ba78acbca0651b0e472,

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",

note = "Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2020",

month = feb,

day = "1",

doi = "10.1007/s00526-019-1690-1",

language = "English (US)",

volume = "59",

journal = "Calculus of Variations and Partial Differential Equations",

issn = "0944-2669",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Hessian estimate for semiconvex solutions to the sigma-2 equation

AU - Shankar, Ravi

AU - Yuan, Yu

PY - 2020/2/1

Y1 - 2020/2/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85077714886&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85077714886&partnerID=8YFLogxK

U2 - 10.1007/s00526-019-1690-1

DO - 10.1007/s00526-019-1690-1

M3 - Article

AN - SCOPUS:85077714886

SN - 0944-2669

VL - 59

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 1

M1 - 30

ER -

Hessian estimate for semiconvex solutions to the sigma-2 equation

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this