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

2024/07/25 by Yawei Wei, Xiaodong Zhou, Wei, Yawei +1
Computer Science · Mathematics · #35B40 #35J70 #47B38 #Analysis of PDEs (math.AP) #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2407.18399

openalex publication_date 2024/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 for 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.

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