Hypoellipticity without loss of derivatives for Fedii's type operators

2017/11/01 by Timur Akhunov, Akhunov, Timur, Lyudmila Korobenko +3
Mathematics · #35A18 #35B65 #35G05 #35H10 #35H20 #35S05 #Advanced Banach Space Theory #Analysis of PDEs (math.AP) #Approximation Theory and Sequence Spaces #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1711.00161

openalex publication_date 2017/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that second order linear operators on ℝ^n+m of the form L(x,y,D_x,D_y) = L₁(x,D_x) + g(x) L₂(y,D_y), where L₁ and L₂ satisfy Morimoto's super-logarithmic estimates and g is smooth, nonnegative, and vanishes only at the origin in ℝⁿ (but to any arbitrary order) are hypoelliptic without loss of derivarives. We also show examples in which our hypotheses are necessary for hypoellipticity.

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