A quantitative second order estimate for (weighted) p-harmonic functions in manifolds under curvature-dimension condition

Jiayin Liu; Shijin Zhang; Yuan Zhou

doi:10.1016/j.jfa.2024.110394

A quantitative second order estimate for (weighted) p-harmonic functions in manifolds under curvature-dimension condition

Jiayin Liu^*
, Shijin Zhang
, Yuan Zhou

^*Corresponding author for this work

School of Mathematical Sciences

University of Jyväskylä
Beijing Normal University

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

Abstract

We build up a quantitative second-order Sobolev estimate of ln⁡w for positive p-harmonic functions w in Riemannian manifolds under Ricci curvature bounded from below and also for positive weighted p-harmonic functions w in weighted manifolds under the Bakry-Émery curvature-dimension condition.

Original language	English
Article number	110394
Journal	Journal of Functional Analysis
Volume	286
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2024.110394
State	Published - 15 May 2024

Keywords

Curvature-dimension condition
Hessian estimate
p-harmonic functions

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10.1016/j.jfa.2024.110394

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@article{44aa61a7dded4075ab9e367112d559e8,

title = "A quantitative second order estimate for (weighted) p-harmonic functions in manifolds under curvature-dimension condition",

abstract = "We build up a quantitative second-order Sobolev estimate of ln⁡w for positive p-harmonic functions w in Riemannian manifolds under Ricci curvature bounded from below and also for positive weighted p-harmonic functions w in weighted manifolds under the Bakry-{\'E}mery curvature-dimension condition.",

keywords = "Curvature-dimension condition, Hessian estimate, p-harmonic functions",

author = "Jiayin Liu and Shijin Zhang and Yuan Zhou",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

year = "2024",

month = may,

day = "15",

doi = "10.1016/j.jfa.2024.110394",

language = "英语",

volume = "286",

journal = "Journal of Functional Analysis",

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T1 - A quantitative second order estimate for (weighted) p-harmonic functions in manifolds under curvature-dimension condition

AU - Liu, Jiayin

AU - Zhang, Shijin

AU - Zhou, Yuan

PY - 2024/5/15

Y1 - 2024/5/15

N2 - We build up a quantitative second-order Sobolev estimate of ln⁡w for positive p-harmonic functions w in Riemannian manifolds under Ricci curvature bounded from below and also for positive weighted p-harmonic functions w in weighted manifolds under the Bakry-Émery curvature-dimension condition.

AB - We build up a quantitative second-order Sobolev estimate of ln⁡w for positive p-harmonic functions w in Riemannian manifolds under Ricci curvature bounded from below and also for positive weighted p-harmonic functions w in weighted manifolds under the Bakry-Émery curvature-dimension condition.

KW - Curvature-dimension condition

KW - Hessian estimate

KW - p-harmonic functions

UR - https://www.scopus.com/pages/publications/85188244517

U2 - 10.1016/j.jfa.2024.110394

DO - 10.1016/j.jfa.2024.110394

M3 - 文章

AN - SCOPUS:85188244517

SN - 0022-1236

VL - 286

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 10

M1 - 110394

ER -

A quantitative second order estimate for (weighted) p-harmonic functions in manifolds under curvature-dimension condition

Abstract

Keywords

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