On the Microlocal Regularity of the Gevrey Vectors for second order partial differential operators with non negative characteristic form of first kind

2024/03/13 by Gregorio Chinni, Chinni, Gregorio, Makhlouf Derridj +1
Mathematics · #35B65 #35H10 #35H20 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2403.08709

openalex publication_date 2024/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the microlocal regularity of the analytic/Gevrey vectors for the following class of second order partial differential equations P(x,D) = ∑_ℓ,j=1ⁿ a_ℓ,j(x) D_ℓ D_j + ∑_ℓ=1ⁿ i b_ℓ(x) D_ℓ +c(x), where a_ℓ,j(x) = a_j,ℓ(x), b_ℓ(x), ℓ,j ∈ \lbrace 1,…, n\rbrace, are real valued real Gevrey functions of order s and c(x) is a Gevrey function of order s, s ≥ 1, on Ω open neighborhood of the origin in ℝⁿ. Thus providing a microlocal version of a result due to M. Derridj in "Gevrey regularity of Gevrey vectors of second order partial differential operators with non negative characteristic form", Complex Anal. Synerg. 6, 10 (2020), https://doi.org/10.1007/s40627-020-00047-8.

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