Weak Harnack inequality for the nonhomogeneous nonlocal equations with general growth

Qi Xue; Ruofang Yang; Chao Zhang

doi:10.3934/mine.2025029

Weak Harnack inequality for the nonhomogeneous nonlocal equations with general growth

Qi Xue
, Ruofang Yang
, Chao Zhang^*

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

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

Abstract

In this paper, we aim to establish a new class of weak Harnack inequalities for weak supersolutions to the nonhomogeneous nonlocal equations with general growth. Our approach mainly relies on the expansion of positivity in the spirit of De Giorgi classes, along with a refined energy estimate.

Original language	English
Pages (from-to)	695-712
Number of pages	18
Journal	Mathematics in Engineering
Volume	7
Issue number	6
DOIs	https://doi.org/10.3934/mine.2025029
State	Published - 2025
Externally published	Yes

Keywords

general growth
nonlocal equations
weak Harnack estimates

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10.3934/mine.2025029

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title = "Weak Harnack inequality for the nonhomogeneous nonlocal equations with general growth",

abstract = "In this paper, we aim to establish a new class of weak Harnack inequalities for weak supersolutions to the nonhomogeneous nonlocal equations with general growth. Our approach mainly relies on the expansion of positivity in the spirit of De Giorgi classes, along with a refined energy estimate.",

keywords = "general growth, nonlocal equations, weak Harnack estimates",

author = "Qi Xue and Ruofang Yang and Chao Zhang",

note = "Publisher Copyright: {\textcopyright} 2025 the Author(s), licensee AIMS Press.",

year = "2025",

doi = "10.3934/mine.2025029",

language = "英语",

volume = "7",

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publisher = "American Institute of Mathematical Sciences",

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T1 - Weak Harnack inequality for the nonhomogeneous nonlocal equations with general growth

AU - Xue, Qi

AU - Yang, Ruofang

AU - Zhang, Chao

PY - 2025

Y1 - 2025

N2 - In this paper, we aim to establish a new class of weak Harnack inequalities for weak supersolutions to the nonhomogeneous nonlocal equations with general growth. Our approach mainly relies on the expansion of positivity in the spirit of De Giorgi classes, along with a refined energy estimate.

AB - In this paper, we aim to establish a new class of weak Harnack inequalities for weak supersolutions to the nonhomogeneous nonlocal equations with general growth. Our approach mainly relies on the expansion of positivity in the spirit of De Giorgi classes, along with a refined energy estimate.

KW - general growth

KW - nonlocal equations

KW - weak Harnack estimates

UR - https://www.scopus.com/pages/publications/105022977652

U2 - 10.3934/mine.2025029

DO - 10.3934/mine.2025029

M3 - 文章

AN - SCOPUS:105022977652

SN - 2640-3501

VL - 7

SP - 695

EP - 712

JO - Mathematics in Engineering

JF - Mathematics in Engineering

IS - 6

ER -

Weak Harnack inequality for the nonhomogeneous nonlocal equations with general growth

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Keywords

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