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arXiv.org e-Print Archive
Preprint . 2024
Data sources: arXiv.org e-Print Archive
Topological Methods in Nonlinear Analysis
Article . 2025 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2024
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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The kernel space of linear operator for a class of Grushin equation

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 11 Dec 2025Embargo end date: 01 Jul 2024Publisher:Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus UniversityJournal:Topological Methods in Nonlinear Analysis (issn: 1230-3429, Copyright policy )
Authors: Yawei Wei; Xiaodong Zhou;

doi: 10.12775/tmna.2025.017 , 10.48550/arxiv.2407.18399

arXiv: 2407.18399

The kernel space of linear operator for a class of Grushin equation

Abstract

In this paper, we concern the kernel of linear operator for a class of Grushin equation. First, we study the kernel space of linear operator for a general Grushin equation. Then, we provide an exact expression for the kernel space of linear operator associated with a special Grushin equation. Finally, we prove the linear operator related to the singularly perturbed Grushin equation is invertible when restricted to the complement of its approximate kernel space.

Keywords

Mathematics - Analysis of PDEs, 35B40, 47B38, 35J70, FOS: Mathematics, Analysis of PDEs (math.AP)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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