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Research Article | Open Access

Weak Harnack inequality for the nonhomogeneous nonlocal equations with general growth

Qi Xue1, Ruofang Yang1, Chao Zhang2( )
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, China
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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

nonlocal equationsweak Harnack estimatesgeneral growth

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Mathematics in Engineering
Volume 7 Issue 6,
December 2025
Pages 695-712
DOI: 10.3934/mine.2025029

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Cite this article:
Xue Q, Yang R, Zhang C. Weak Harnack inequality for the nonhomogeneous nonlocal equations with general growth. Mathematics in Engineering, 2025, 7(6): 695-712. https://doi.org/10.3934/mine.2025029

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Received: 03 September 2025
Revised: 08 November 2025
Accepted: 24 November 2025
Published: 15 December 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)