Weak Harnack inequalities for eigenvalues and constant rank theorems

Gábor Székelyhidi; Ben Weinkove

doi:10.1080/03605302.2021.1892755

Weak Harnack inequalities for eigenvalues and constant rank theorems

Gábor Székelyhidi, Ben Weinkove^*

^*Corresponding author for this work

Mathematics

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

5 Scopus citations

Abstract

We consider convex solutions of nonlinear elliptic equations which satisfy the structure condition of Bian and Guan. We prove a weak Harnack inequality for the eigenvalues of the Hessian of these solutions. This can be viewed as a quantitative version of the constant rank theorem.

Original language	English (US)
Pages (from-to)	1585-1600
Number of pages	16
Journal	Communications in Partial Differential Equations
Volume	46
Issue number	8
DOIs	https://doi.org/10.1080/03605302.2021.1892755
State	Published - 2021

Keywords

Constant rank, convexity
Harnack inequality

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/03605302.2021.1892755

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title = "Weak Harnack inequalities for eigenvalues and constant rank theorems",

abstract = "We consider convex solutions of nonlinear elliptic equations which satisfy the structure condition of Bian and Guan. We prove a weak Harnack inequality for the eigenvalues of the Hessian of these solutions. This can be viewed as a quantitative version of the constant rank theorem.",

keywords = "Constant rank, convexity, Harnack inequality",

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

note = "Funding Information: Supported in part by National Science Foundation grants DMS-1906216 and DMS-2005311. Part of this work was carried out while the second-named author was visiting the Department of Mathematical Sciences at the University of Memphis and he thanks them for their kind hospitality. Publisher Copyright: {\textcopyright} 2021 Taylor & Francis Group, LLC.",

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T1 - Weak Harnack inequalities for eigenvalues and constant rank theorems

AU - Székelyhidi, Gábor

AU - Weinkove, Ben

N1 - Funding Information: Supported in part by National Science Foundation grants DMS-1906216 and DMS-2005311. Part of this work was carried out while the second-named author was visiting the Department of Mathematical Sciences at the University of Memphis and he thanks them for their kind hospitality. Publisher Copyright: © 2021 Taylor & Francis Group, LLC.

PY - 2021

Y1 - 2021

N2 - We consider convex solutions of nonlinear elliptic equations which satisfy the structure condition of Bian and Guan. We prove a weak Harnack inequality for the eigenvalues of the Hessian of these solutions. This can be viewed as a quantitative version of the constant rank theorem.

AB - We consider convex solutions of nonlinear elliptic equations which satisfy the structure condition of Bian and Guan. We prove a weak Harnack inequality for the eigenvalues of the Hessian of these solutions. This can be viewed as a quantitative version of the constant rank theorem.

KW - Constant rank, convexity

KW - Harnack inequality

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DO - 10.1080/03605302.2021.1892755

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JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

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ER -

Weak Harnack inequalities for eigenvalues and constant rank theorems

Abstract

Keywords

ASJC Scopus subject areas

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