On a constant rank theorem for nonlinear elliptic PDES

Gábor Székelyhidi; Ben Weinkove

doi:10.3934/dcds.2016081

On a constant rank theorem for nonlinear elliptic PDES

Gábor Székelyhidi, Ben Weinkove^*

^*Corresponding author for this work

Mathematics

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

10 Scopus citations

Abstract

We give a new proof of Bian-Guan's constant rank theorem for nonlinear elliptic equations. Our approach is to use a linear expression of the eigenvalues of the Hessian instead of quotients of elementary symmetric functions.

Original language	English (US)
Pages (from-to)	6523-6532
Number of pages	10
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	36
Issue number	11
DOIs	https://doi.org/10.3934/dcds.2016081
State	Published - Nov 2016

Keywords

Constant rank Hessian
Eigenvalues
Nonlinear elliptic

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2016081

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abstract = "We give a new proof of Bian-Guan's constant rank theorem for nonlinear elliptic equations. Our approach is to use a linear expression of the eigenvalues of the Hessian instead of quotients of elementary symmetric functions.",

keywords = "Constant rank Hessian, Eigenvalues, Nonlinear elliptic",

author = "G{\'a}bor Sz{\'e}kelyhidi and Ben Weinkove",

note = "Funding Information: Supported in part by National Science Foundation grants DMS-1306298 and DMS-1350696 (G.Sz.) and DMS-1406164 (B.W.). Part of this work was carried out while the first-named author was visiting the Mathematics Department of Northwestern University and he thanks them for their hospitality. Publisher Copyright: {\textcopyright} 2016, Southwest Missouri State University. All rights reserved.",

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AU - Székelyhidi, Gábor

AU - Weinkove, Ben

N1 - Funding Information: Supported in part by National Science Foundation grants DMS-1306298 and DMS-1350696 (G.Sz.) and DMS-1406164 (B.W.). Part of this work was carried out while the first-named author was visiting the Mathematics Department of Northwestern University and he thanks them for their hospitality. Publisher Copyright: © 2016, Southwest Missouri State University. All rights reserved.

PY - 2016/11

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N2 - We give a new proof of Bian-Guan's constant rank theorem for nonlinear elliptic equations. Our approach is to use a linear expression of the eigenvalues of the Hessian instead of quotients of elementary symmetric functions.

AB - We give a new proof of Bian-Guan's constant rank theorem for nonlinear elliptic equations. Our approach is to use a linear expression of the eigenvalues of the Hessian instead of quotients of elementary symmetric functions.

KW - Constant rank Hessian

KW - Eigenvalues

KW - Nonlinear elliptic

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On a constant rank theorem for nonlinear elliptic PDES

Abstract

Keywords

ASJC Scopus subject areas

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