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Harnack inequality for the nonlocal equations with general growth

Published online by Cambridge University Press:  23 August 2022

Yuzhou Fang
Affiliation:
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China (18b912036@hit.edu.cn)
Chao Zhang
Affiliation:
School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, China (czhangmath@hit.edu.cn)

Abstract

We consider a class of generalized nonlocal $p$-Laplacian equations. We find some proper structural conditions to establish a version of nonlocal Harnack inequalities of weak solutions to such nonlocal problems by using the expansion of positivity and energy estimates.

Type
Research Article
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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