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Harnack inequality for the nonlocal equations with general growth

Part of: Miscellaneous topics - Partial differential equations Partial differential equations Integral, integro-differential, and pseudodifferential operators Linear function spaces and their duals Representations of solutions

Published online by Cambridge University Press:  23 August 2022

Yuzhou Fang  and
Chao Zhang Open the ORCID record for Chao Zhang [Opens in a new window]
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)
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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.

Keywords

Expansion of positivityfractional Orlicz–Sobolev spacegeneral growthHarnack inequalitynonlocal equations

MSC classification

Primary: 35R11: Fractional partial differential equations
Secondary: 47G20: Integro-differential operators 35B65: Smoothness and regularity of solutions 35D30: Weak solutions 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 5 , October 2023 , pp. 1479 - 1502
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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